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Question
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Solution
Given : `cos A + cos^2 A = 1`
we have to prove `sin^2 A + sin^4 A = 1`
Now
`cos A + cos^2 A = 1`
`=>cos A = 1 - cos^2 A`
`=> cos A = sin^2 A`
`=> sin^2 A = cos A`
Therefore, we have
`sin^2 A + sin^4 A = cos A + (cos A)^2`
`= cos A + cos^`2 A`
= 1
Hence proved.
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