Question:
Prove that
$\cos 2 x+2 \sin ^{2} x=1$
Solution:
To Prove: $\cos 2 x+2 \sin ^{2} x=1$
Taking LHS,
$=\cos 2 x+2 \sin ^{2} x$
$=\left(2 \cos ^{2} x-1\right)+2 \sin ^{2} x\left[\because 1+\cos 2 x=2 \cos ^{2} x\right]$
$=2\left(\cos ^{2} x+\sin ^{2} x\right)-1$
$=2(1)-1\left[\because \cos ^{2} \theta+\sin ^{2} \theta=1\right]$
$=2-1$
$=1$
= RHS
∴ LHS = RHS
Hence Proved
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