Question

sin raise to power 4 theta + Cos raise to power 4 theta upon 1 minus 2 sin square theta cos square theta equals to 1​

Answer 1

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Answer 2

$\dfrac{\sin^4 \theta+\cos^4 \theta}{1-2\sin^2 \theta\cos^2 \theta}=1$, proved.

Step-by-step explanation:

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

L.H.S.$=\dfrac{\sin^4 \theta+\cos^4 \theta}{1-2\sin^2 \theta\cos^2 \theta}$

$=\dfrac{(\sin^2 \theta+\cos^2 \theta)^2-2\sin^2 \theta\cos^2 \theta}{1-2\sin^2 \theta\cos^2 \theta}$

Since, $(a+b)^{2}=a^{2} +b^{2} +2ab$

⇒ $a^{2} +b^{2}=(a+b)^{2}-2ab$

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

[ ∵ $\sin^2 \theta+\cos^2 \theta=1$]

$=\dfrac{1-2\sin^2 \theta\cos^2 \theta}{1-2\sin^2 \theta\cos^2 \theta}$

= 1 = R.H.S., proved.

Hence, $\dfrac{\sin^4 \theta+\cos^4 \theta}{1-2\sin^2 \theta\cos^2 \theta}=1$, proved.