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  • If cosA + cos power 2 A = 1, then sin power 2 A + sin power 4 A = 1.

If cosA + cos2A = 1, then sin2A + sin4A = 1.

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best_answer

Given
cosA + cos2A = 1        …(1) 
cos A = 1 – cos2A
cosA = sin2A          …(2)    (\because sin2 \theta = 1 – cos2\theta)
\sin ^{2} A+\sin ^{4}A= 1
L.H.S.

\sin ^{2} A+\sin ^{4}A
\sin ^{2} A+ \left ( \sin ^{2}A \right )^{2}
 \cos A+\left ( \cos A \right )^{2} (from (2))
cosA + cos2A
= 1       (R.H.S.)           (from (1))
Hence sin2A + sin4A = 1
So, the given statement is true.

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infoexpert27

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