Question
Prove the following trigonometric identities.
$\tan^2\theta\cos^2\theta=1-\cos^2\theta$
$\tan^2\theta\cos^2\theta=1-\cos^2\theta$
✓
Answer
We know that, $\sin^2\theta+\cos^2\theta=1$ So, $\text{L.H.S.} = \tan^2\theta\cos^2\theta$ $\tan^2\theta\cos^2\theta=(\tan\theta\times\cos\theta)^2$ $=\Big(\frac{\sin\theta}{\cos\theta}\times\cos\theta\Big)^2$ $=(\sin\theta)^2$ $=\sin^2\theta$$=1-\cos^2\theta = \text{R.H.S.}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$
$\therefore\ \text{L.H.S}=\text{R.H.S}$
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