Question

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Answer 1

Step-by-step explanation:

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Answer 2

$\sin^4 \theta-\cos^4 \theta=1-2\cos^2 \theta$, proved.

Step-by-step explanation:

To prove that, $\sin^4 \theta-\cos^4 \theta=1-2\cos^2 \theta$.

L.H.S. = $\sin^4 \theta-\cos^4 \theta$

= $(\sin^2 \theta)^2-(\cos^2 \theta)^2$

Using the algebraic identity,

$a^{2}-b^{2}=(a+b)(a-b)$

= $(\sin^2 \theta+\cos^2 \theta)(\sin^2 \theta-\cos^2 \theta)$

Using the trigonometric identity,

$\sin^2 A+\cos^2 A$ = 1

= $(1)(\sin^2 \theta-\cos^2 \theta)$

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

Using the trigonometric identity,

$\sin^2 A+\cos^2 A$ = 1

⇒ $\sin^2 A =1-\cos^2 A$

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

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

= R.H.S., proved.

Thus, $\sin^4 \theta-\cos^4 \theta=1-2\cos^2 \theta$, proved.