Question

8. sin4 theta + sin2 theta cos2 theta= sin2 theta​

Answer 1

Answer:

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Answer 2

ANSWER:

To Prove:

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

Proof:

We need to prove that,

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

Taking and Solving LHS,

$\implies\sin^4\theta + \sin^2\theta\cos^2\theta$

Now, we will take sin²ө common in both terms. So,

$\implies\sin^4\theta + \sin^2\theta\cos^2\theta$

$\implies\sin^2\theta(\sin^2\theta+\cos^2\theta)$

We know that,

⇒ sin²ө + cos²ө = 1

So,

$\implies\sin^2\theta(\sin^2\theta+\cos^2\theta)$

$\implies\sin^2\theta(1)$

$\bf\implies\sin^2\theta = RHS$

As, LHS = RHS,

Hence Proved!!!!

Learn More:

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