Question

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Answer 1

Answer :-

$\sf sin^4\theta + sin^2 \theta \cos^2 \theta = sin^2\theta$

By using the identity :-

$\sf cos^2 \theta = 1 - sin^2 \theta$

$\sf sin^4\theta + sin^2 \theta ( 1 - sin^2\theta)$

$\sf = sin^4\theta + sin^2\theta - (sin^2\theta)(sin^2\theta)$

$\sf = \cancel{sin^4\theta} + sin^2\theta - \cancel{sin^4\theta}$

$\sf = sin^2\theta = sin^2\theta$

LHS = RHS

Hence proved

Trigonometric Identities :-

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{minipage}}$