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First Year Math Trigonometric Identities


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Class 9Class 10First YearSecond Year
1. Prove thatv) \cos \left(270^{\circ}+\theta\right)=\sin \theta
1. Prove thatv)   \cos \left(270^{\circ}+\theta\right)=\sin \theta

1.Provethatv)cos(270+θ)=sinθ1. Prove thatv) \cos \left(270^{\circ}+\theta\right)=\sin \theta

3. Prove that:ii) \cos \left(\alpha+45^{\circ}\right)=\frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)
3. Prove that:ii)   \cos \left(\alpha+45^{\circ}\right)=\frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)

3.Provethat:ii)cos(α+45)=12(cosαsinα)3. Prove that:ii) \cos \left(\alpha+45^{\circ}\right)=\frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)

2. Express the following sums or differences as products:ii) \sin 8 \theta-\sin 4 \theta
2. Express the following sums or differences as products:ii)  \sin 8 \theta-\sin 4 \theta

2.Expressthefollowingsumsordifferencesasproducts:ii)sin8θsin4θ2. Express the following sums or differences as products:ii) \sin 8 \theta-\sin 4 \theta

Example 5: If \alpha \beta \gamma are the angles of \triangle A B C prove that:i) \tan \alpha+\tan \beta+\tan \gamma=\tan \alpha \tan \beta \tan \gamma
Example 5: If  \alpha \beta \gamma  are the angles of  \triangle A B C  prove that:i)  \tan \alpha+\tan \beta+\tan \gamma=\tan \alpha \tan \beta \tan \gamma

Example5:IfαβγaretheanglesofABCprovethat:i)tanα+tanβ+tanγ=tanαtanβtanγExample 5: If \alpha \beta \gamma are the angles of \triangle A B C prove that:i) \tan \alpha+\tan \beta+\tan \gamma=\tan \alpha \tan \beta \tan \gamma

Prove the following identities:3. \frac{\sin 2 \alpha}{1+\cos 2 \alpha}=\tan \alpha
Prove the following identities:3.  \frac{\sin 2 \alpha}{1+\cos 2 \alpha}=\tan \alpha

Provethefollowingidentities:3.sin2α1+cos2α=tanαProve the following identities:3. \frac{\sin 2 \alpha}{1+\cos 2 \alpha}=\tan \alpha

9. If \sin \alpha=\frac{4}{5}< and \sin \beta=\frac{12}{13}< where \frac{\pi}{2} \alpha \pi and \frac{\pi}{2} \beta \pi . Findii) \cos (\alpha+\beta) In which rants do the terminal sides of the angles of measures (\alpha+\beta) and (\alpha-\beta) lie?
9. If  \sin \alpha=\frac{4}{5}<  and  \sin \beta=\frac{12}{13}<  where  \frac{\pi}{2}  \alpha  \pi  and  \frac{\pi}{2}  \beta  \pi . Findii)   \cos (\alpha+\beta) In which rants do the terminal sides of the angles of measures  (\alpha+\beta)  and  (\alpha-\beta)  lie?

9.Ifsinα=45<andsinβ=1213<whereπ2απandπ2βπ.Findii)cos(α+β)Inwhichrantsdotheterminalsidesoftheanglesofmeasures(α+β)and(αβ)lie?9. If \sin \alpha=\frac{4}{5}< and \sin \beta=\frac{12}{13}< where \frac{\pi}{2} \alpha \pi and \frac{\pi}{2} \beta \pi . Findii) \cos (\alpha+\beta) In which rants do the terminal sides of the angles of measures (\alpha+\beta) and (\alpha-\beta) lie?

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