Trigonometric identities – Questions ( 11 – 20)
Question No: 1
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Show that \( \frac{\sin 2 \theta}{\sin \theta}-\frac{\cos 2 \theta}{\cos \theta}\)\( =\tan \theta\) |
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Question No: 2
| . Prove that \( \frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=\frac{2}{\sin A}\) . |
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Question No: 3
| . Prove that \( \frac{1}{\tan x}+\tan x=\frac{1}{\sin x \cos x}\) . |
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Question No: 4
| . Prove that \( \frac{\cos x}{1 +\sin x}+\frac{1+\sin x}{\cos x}=\frac{2}{\cos x}\) . |
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Question No: 5
| . Prove that \( \frac{\sin ^2 x+4 \sin x+3}{\cos ^2 x}=\frac{3+\sin x}{1-\sin x}\) . |
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Question No: 6
| . Prove that \(1-2 \cos ^2 x=\frac{\tan ^2 x-1}{\tan ^2 x+1}\) . |
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Question No: 7
| . Prove that \( \frac{\tan ^2 x}{\tan ^2 x+1}=\sin ^2 x\) . |
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Question No: 8
| . Prove that \( \frac{\sin ^4 x-\cos ^4 x}{\sin ^2 x-\cos ^2 x}=1\) . |
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Question No: 9
| . Prove that \( (2 \sin \theta+3 \cos \theta)^2+(3 \sin \theta-2 \cos \theta)^2=13\) . |
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Question No: 10
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Show that \( \frac{\sin \theta+\sin 2 \theta}{1+\cos \theta+\cos 2 \theta}\)\( =\tan \theta\) |
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Question No: 11
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Show that \( \frac{\sin 2 \theta}{\sin \theta}-\frac{\cos 2 \theta}{\cos \theta}\)\( =\tan \theta\) |
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