If cos A + cos2 A = 1, then (sin2 A + sin4 A) = ?
Question:

If cos A + cos2 A = 1, then (sin2 A + sin4 A) = ?
(a) 1
(b) 2
(c) 3
(d) 4

 

Solution:

(a) 1

$\cos A+\cos ^{2} A=1$

$=>\cos A=1-\cos ^{2} A$

$=>\cos A=\sin ^{2} A \quad\left(\because 1-\cos ^{2} A=\sin ^{2}\right)$

$=>\cos ^{2} A=\sin ^{4} A \quad$ (Squaring both sides)

$=>1-\sin ^{2} A=\sin ^{4} A$

 

$=>\sin ^{4} A+\sin ^{2} A=1$

 

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