Prove that ^2 + ^4 = ^2 + ^4 . - Vidyadip

Question

Prove that $\sin^2\theta + \cos^4 \theta = \cos^2\theta + \sin^4 \theta .$

✓

Answer

$L.H.S. = \sin^2\theta + \cos^4 \theta$
$= 1 - \cos^2 \theta + \cos^4 \theta$
$= 1 - \cos^2 \theta (1 - \cos^2 \theta )$
$= 1 - (1 - \sin^2 \theta ) \sin^2 \theta$
$= 1 - \sin^2 \theta + \sin^4 \theta$
$= \cos^2 \theta + \sin^4 \theta$
$= R.H.S.$
Hence proved.

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