Question:
If sin A + sin2 A = 1, then (cos2 A + cos4 A) = ?
(a) $\frac{1}{2}$
(b) 1
(c) 2
(d) 3
Solution:
(b) 1
$\sin A+\sin ^{2} A=1$
$=>\sin A=1-\sin ^{2} A$
$=>\sin A=\cos ^{2} A \quad\left(\because 1-\sin ^{2} A\right)$
$=>\sin ^{2} A=\cos ^{4} A \quad$ (Squaring both sides)
$=>1-\cos ^{2} A=\cos ^{4} A$
$=>\cos ^{4} A+\cos ^{2} A=1$
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