First Year Math Inverse Trigonometric Functions

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Class 9Class 10First YearSecond Year
Q.4Tan1(3)=(a)2π3(b)2π3(c)π6(d)π3LahoreBoard2010Q.4 \operatorname{Tan}^{-1}(-\sqrt{3})= (a) \frac{2 \pi}{3} (b) -\frac{2 \pi}{3} (c) -\frac{\pi}{6} (d) -\frac{\pi}{3} Lahore Board 2010

Q.21 \operatorname{Tan}^{-1} \frac{1}{2}+\operatorname{Tan}^{-1} \frac{1}{3}= (a) \frac{\pi}{6} (b) \frac{\pi}{4} (c) \frac{\pi}{2} (d) \pi Gujrantwala Board; 2008
Q.21  \operatorname{Tan}^{-1} \frac{1}{2}+\operatorname{Tan}^{-1} \frac{1}{3}= (a)  \frac{\pi}{6} (b)  \frac{\pi}{4} (c)  \frac{\pi}{2} (d)  \pi Gujrantwala Board; 2008

Q.21Tan112+Tan113=(a)π6(b)π4(c)π2(d)πGujrantwalaBoard;2008Q.21 \operatorname{Tan}^{-1} \frac{1}{2}+\operatorname{Tan}^{-1} \frac{1}{3}= (a) \frac{\pi}{6} (b) \frac{\pi}{4} (c) \frac{\pi}{2} (d) \pi Gujrantwala Board; 2008

16. \tan 28 \cot \theta=3
16.  \tan 28 \cot \theta=3

16.tan28cotθ=316. \tan 28 \cot \theta=3

11. \operatorname{Tan}^{-1} \frac{1}{13}+\operatorname{Tan}^{-1} \frac{1}{4}=\operatorname{Tan}^{-1} \frac{1}{3}
11.  \operatorname{Tan}^{-1} \frac{1}{13}+\operatorname{Tan}^{-1} \frac{1}{4}=\operatorname{Tan}^{-1} \frac{1}{3}

11.Tan1113+Tan114=Tan11311. \operatorname{Tan}^{-1} \frac{1}{13}+\operatorname{Tan}^{-1} \frac{1}{4}=\operatorname{Tan}^{-1} \frac{1}{3}

8. Find \sin \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{4}{5}\right) Prove that
8. Find  \sin \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{4}{5}\right)  Prove that

8.Findsin(sin135+sin145)Provethat8. Find \sin \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{4}{5}\right) Prove that

\[\sin \left(\cos ^{-1} \theta+\sin ^{-1} \theta\right)=\text { ? }\]A. 4B. 3C. 2D. 1
\[\sin \left(\cos ^{-1} \theta+\sin ^{-1} \theta\right)=\text { ? }\]A. 4B. 3C. 2D. 1

\[\sin \left(\cos ^{-1} \theta+\sin ^{-1} \theta\right)=\text { ? }\]A. 4B. 3C. 2D. 1

Example 3. Solve 2 \sin ^{2} \theta+2 \sqrt{2} \sin \theta-3=0 .
Example 3. Solve  2 \sin ^{2} \theta+2 \sqrt{2} \sin \theta-3=0 .

Example3.Solve2sin2θ+22sinθ3=0.Example 3. Solve 2 \sin ^{2} \theta+2 \sqrt{2} \sin \theta-3=0 .

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