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Question
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Options
−1
0
1
None of these
Solution
Given:
`cos A+cos^2 A=1`
`⇒ 1- cos^2 A= cos A`
So,
`sin^2 A+sin^4 A`
`= sin^2 A+sin^2 A sin^2 A`
`= sin^2 A+(1-cos^2 A)(1-cos^2 A)`
`=sin^2 A+cos A cos A`
`=sin^2 A+cos^2 A`
`=1`
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