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First Year Math Solutions Of Trigonometric Equations 1. Find the solutions of the following equations which lie in [02 \pi] iv) \cot \theta=\frac{1}{\sqrt{3}}


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Class 9Class 10First YearSecond Year
1. Find the solutions of the following equations which lie in [02 \pi] iv) \cot \theta=\frac{1}{\sqrt{3}}

2. Solve the following trigonometric equations:ii) \operatorname{cosec}^{2} \theta=\frac{4}{3}
2. Solve the following trigonometric equations:ii)  \operatorname{cosec}^{2} \theta=\frac{4}{3}

2. Solve the following trigonometric equations:ii) \operatorname{cosec}^{2} \theta=\frac{4}{3}

7. 3 \cos ^{2} \theta-2 \sqrt{3} \sin \theta \cos \theta-3 \sin ^{2} \theta=0 [Hint: Divide by \sin ^{2} \theta ]
7.  3 \cos ^{2} \theta-2 \sqrt{3} \sin \theta \cos \theta-3 \sin ^{2} \theta=0 [Hint: Divide by  \sin ^{2} \theta  ]

7. 3 \cos ^{2} \theta-2 \sqrt{3} \sin \theta \cos \theta-3 \sin ^{2} \theta=0 [Hint: Divide by \sin ^{2} \theta ]

Q.24 Solution of equation \tan x=\frac{1}{\sqrt{3}} is in:(a) I \& Il Lahore Board; 2015(b) I \& ll (c) 11 \& 1 \mathrm{~V} (d) I
Q.24 Solution of equation  \tan x=\frac{1}{\sqrt{3}}  is in:(a) I \& Il  Lahore Board; 2015(b) I \& ll (c)  11 \& 1 \mathrm{~V}  (d) I

Q.24 Solution of equation \tan x=\frac{1}{\sqrt{3}} is in:(a) I \& Il Lahore Board; 2015(b) I \& ll (c) 11 \& 1 \mathrm{~V} (d) I

6. 2 \sin ^{2} \theta-\sin \theta=0
6.  2 \sin ^{2} \theta-\sin \theta=0

6. 2 \sin ^{2} \theta-\sin \theta=0

4. \tan ^{2} \theta-\sec \theta-1=0
4.  \tan ^{2} \theta-\sec \theta-1=0

4. \tan ^{2} \theta-\sec \theta-1=0

Q.6 Solution of 1+\cos x=0 is :(a) \frac{\pi}{2} (b) \pi (c) 2 \pi (d) none of theseGujranwala Board 2013; Lahore Board 2015; 2005
Q.6 Solution of  1+\cos x=0  is :(a)  \frac{\pi}{2} (b)  \pi (c)  2 \pi (d) none of theseGujranwala Board 2013; Lahore Board 2015; 2005

Q.6 Solution of 1+\cos x=0 is :(a) \frac{\pi}{2} (b) \pi (c) 2 \pi (d) none of theseGujranwala Board 2013; Lahore Board 2015; 2005

Q.9 Solutions of the equation 1+\cos \theta=0 are in rants(a) II \& III(b) 1 \& \mathrm{NV} (c) \|\&\| \mathrm{V} (d) none of these
Q.9 Solutions of the equation  1+\cos \theta=0  are in rants(a) II \& III(b)  1 \& \mathrm{NV} (c)  \|\&\| \mathrm{V} (d) none of these

Q.9 Solutions of the equation 1+\cos \theta=0 are in rants(a) II \& III(b) 1 \& \mathrm{NV} (c) \|\&\| \mathrm{V} (d) none of these

Example 1: Solve: \sin x+\cos x=0
Example 1: Solve:  \sin x+\cos x=0

Example 1: Solve: \sin x+\cos x=0

Q.18 If one solution of \cos x=1 in x \in[02 \pi] is zero then other is(a) \frac{\pi}{2} (b) \pi (c) -\pi (d) 2 \pi
Q.18 If one solution of  \cos x=1  in  x \in[02 \pi]  is zero then other is(a)  \frac{\pi}{2} (b)  \pi (c)  -\pi (d)  2 \pi

Q.18 If one solution of \cos x=1 in x \in[02 \pi] is zero then other is(a) \frac{\pi}{2} (b) \pi (c) -\pi (d) 2 \pi

Q.1 An equation containing at least one trigonometric function is called :(a) algebraic equation(b) ratic equation(c) linear equation(d) Trigonometric equation
Q.1 An equation containing at least one trigonometric function is called :(a) algebraic equation(b) ratic equation(c) linear equation(d) Trigonometric equation

Q.1 An equation containing at least one trigonometric function is called :(a) algebraic equation(b) ratic equation(c) linear equation(d) Trigonometric equation

Find the solution sets of the following equations:15. \sin x+\cos 3 x=\cos 5 x
Find the solution sets of the following equations:15.  \sin x+\cos 3 x=\cos 5 x

Find the solution sets of the following equations:15. \sin x+\cos 3 x=\cos 5 x

Find the solution sets of the following equations:18. \sin x+\sin 3 x+\sin 5 x=0
Find the solution sets of the following equations:18.  \sin x+\sin 3 x+\sin 5 x=0

Find the solution sets of the following equations:18. \sin x+\sin 3 x+\sin 5 x=0

Q.13 If \cos x=\frac{1}{\sqrt{2}} then reference angle is :(a) \frac{\pi}{3} (b) \frac{\pi}{4} (c) \frac{\pi}{6} (d) -\frac{\pi}{6} Lahore Board 2014
Q.13 If  \cos x=\frac{1}{\sqrt{2}}  then reference angle is :(a)  \frac{\pi}{3} (b)  \frac{\pi}{4} (c)  \frac{\pi}{6} (d)  -\frac{\pi}{6} Lahore Board 2014

Q.13 If \cos x=\frac{1}{\sqrt{2}} then reference angle is :(a) \frac{\pi}{3} (b) \frac{\pi}{4} (c) \frac{\pi}{6} (d) -\frac{\pi}{6} Lahore Board 2014

Find the solution sets of the following equations:20. \cos \theta+\cos 3 \theta+\cos 5 \theta+\cos 7 \theta=0
Find the solution sets of the following equations:20.  \cos \theta+\cos 3 \theta+\cos 5 \theta+\cos 7 \theta=0

Find the solution sets of the following equations:20. \cos \theta+\cos 3 \theta+\cos 5 \theta+\cos 7 \theta=0

Q.14 If \sin x=\frac{\sqrt{3}}{2} then the reference angle is :(a) \frac{\pi}{6} (b) \frac{\pi}{4} (c) \frac{\pi}{3} (d) \frac{\pi}{2}
Q.14 If  \sin x=\frac{\sqrt{3}}{2}  then the reference angle is :(a)  \frac{\pi}{6} (b)  \frac{\pi}{4} (c)  \frac{\pi}{3} (d)  \frac{\pi}{2}

Q.14 If \sin x=\frac{\sqrt{3}}{2} then the reference angle is :(a) \frac{\pi}{6} (b) \frac{\pi}{4} (c) \frac{\pi}{3} (d) \frac{\pi}{2}

Q.8 If \sin x+\cos x=0 then x= (a) \frac{\pi}{4}-\frac{\pi}{4} (b) -\frac{\pi}{4}-\frac{\pi}{2} (c) -\frac{\pi}{4} \frac{3 \pi}{4} (d) none of theseLahore Board 2004
Q.8 If  \sin x+\cos x=0  then  x= (a)  \frac{\pi}{4}-\frac{\pi}{4} (b)  -\frac{\pi}{4}-\frac{\pi}{2} (c)  -\frac{\pi}{4} \frac{3 \pi}{4} (d) none of theseLahore Board 2004

Q.8 If \sin x+\cos x=0 then x= (a) \frac{\pi}{4}-\frac{\pi}{4} (b) -\frac{\pi}{4}-\frac{\pi}{2} (c) -\frac{\pi}{4} \frac{3 \pi}{4} (d) none of theseLahore Board 2004

1. Find the solutions of the following equations which lie in [02 \pi] iii) \sec x=-2
1. Find the solutions of the following equations which lie in  [02 \pi] iii)  \sec x=-2

1. Find the solutions of the following equations which lie in [02 \pi] iii) \sec x=-2

Q.11 If \theta=150^{\circ} then its reference angle is:(a) 15^{\circ} (b) 30^{\circ} (c) 45^{\circ} (d) 60^{\circ} FalsalabadBoard 2012
Q.11 If  \theta=150^{\circ}  then its reference angle is:(a)  15^{\circ} (b)  30^{\circ} (c)  45^{\circ} (d)  60^{\circ} FalsalabadBoard 2012

Q.11 If \theta=150^{\circ} then its reference angle is:(a) 15^{\circ} (b) 30^{\circ} (c) 45^{\circ} (d) 60^{\circ} FalsalabadBoard 2012

2. Solve the following trigonometric equations:iii) \sec ^{2} \theta=\frac{4}{3}
2. Solve the following trigonometric equations:iii)  \sec ^{2} \theta=\frac{4}{3}
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2. Solve the following trigonometric equations:iii) \sec ^{2} \theta=\frac{4}{3}

1. Find the solutions of the following equations which lie in [02 \pi] i) \sin x=-\frac{\sqrt{3}}{2}
1. Find the solutions of the following equations which lie in  [02 \pi] i)  \sin x=-\frac{\sqrt{3}}{2}
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1. Find the solutions of the following equations which lie in [02 \pi] i) \sin x=-\frac{\sqrt{3}}{2}

Example 5: Solve the equation: \csc x=\sqrt{3}+\cot x
Example 5: Solve the equation:  \csc x=\sqrt{3}+\cot x
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Example 5: Solve the equation: \csc x=\sqrt{3}+\cot x

Find the solution sets of the following equations:19. \sin \theta+\sin 3 \theta+\sin 5 \theta+\sin 7 \theta=0
Find the solution sets of the following equations:19.  \sin \theta+\sin 3 \theta+\sin 5 \theta+\sin 7 \theta=0
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Find the solution sets of the following equations:19. \sin \theta+\sin 3 \theta+\sin 5 \theta+\sin 7 \theta=0

1. Find the solutions of the following equations which lie in [02 \pi] iii) \sec x=-2
1. Find the solutions of the following equations which lie in  [02 \pi] iii)  \sec x=-2
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1. Find the solutions of the following equations which lie in [02 \pi] iii) \sec x=-2

1. Find the solutions of the following equations which lie in [02 \pi] iv) \cot \theta=\frac{1}{\sqrt{3}}
1. Find the solutions of the following equations which lie in  [02 \pi] iv)  \cot \theta=\frac{1}{\sqrt{3}}
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1. Find the solutions of the following equations which lie in [02 \pi] iv) \cot \theta=\frac{1}{\sqrt{3}}

Q.10 Reference angle lies in rant:(a) 1(b) 11(c) 111(d) 1 \mathrm{~V}
Q.10 Reference angle lies in rant:(a) 1(b) 11(c) 111(d)  1 \mathrm{~V}
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Q.10 Reference angle lies in rant:(a) 1(b) 11(c) 111(d) 1 \mathrm{~V}

Example 2: Solve the equation: 1+\cos x=0
Example 2: Solve the equation:  1+\cos x=0
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Example 2: Solve the equation: 1+\cos x=0

Q.5 If \sin x=-\frac{\sqrt{3}}{2} then solution is(a) \frac{4 \pi}{6} \frac{5 \pi}{6} (b) \frac{4 \pi}{3} \frac{5 \pi}{3} (c) \frac{5 \pi}{6} \frac{7 \pi}{6} (d) \frac{\pi}{3} \frac{7 \pi}{3} Rawalpindl Board 2013
Q.5 If  \sin x=-\frac{\sqrt{3}}{2}  then solution is(a)  \frac{4 \pi}{6} \frac{5 \pi}{6} (b)  \frac{4 \pi}{3} \frac{5 \pi}{3} (c)  \frac{5 \pi}{6} \frac{7 \pi}{6} (d)  \frac{\pi}{3} \frac{7 \pi}{3} Rawalpindl Board 2013
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Q.5 If \sin x=-\frac{\sqrt{3}}{2} then solution is(a) \frac{4 \pi}{6} \frac{5 \pi}{6} (b) \frac{4 \pi}{3} \frac{5 \pi}{3} (c) \frac{5 \pi}{6} \frac{7 \pi}{6} (d) \frac{\pi}{3} \frac{7 \pi}{3} Rawalpindl Board 2013

3. 3 \tan ^{2} \theta+2 \sqrt{3} \tan \theta+1=0
3.   3 \tan ^{2} \theta+2 \sqrt{3} \tan \theta+1=0
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3. 3 \tan ^{2} \theta+2 \sqrt{3} \tan \theta+1=0

Find the solution sets of the following equations:14. \sin 4 x-\sin 2 x=\cos 3 x
Find the solution sets of the following equations:14.  \sin 4 x-\sin 2 x=\cos 3 x
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Find the solution sets of the following equations:14. \sin 4 x-\sin 2 x=\cos 3 x

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