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We have,
sinA + sin2A = 1 ...(1)
⇒ sinA = 1 – sin2A ...(2)
Now
cos2A + cos4A
= (1 – sin2A) + {(1 – sin2A)}2
= sinA + sin2A [from (2)]
= 1 [from (1)]
Regards
Arun (askIITians forum expert)
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