# If sinθ + sin2θ = 1, then prove that cos2θ +1 cos4θ = 1

Given : sin θ + sin2 θ = 1

sin θ = 1 sin2 θ

Taking LHS = cos2+ cos4

= cos2 θ + (cos2 θ)2

= (1– sin2 θ) + (1– sin2 θ)2 …(i)

Putting sin θ = 1 – sin2 θ in Eq. (i), we get

= sin θ + (sin θ)2

= sin θ + sin2 θ

= 1 [Given: sin θ + sin2 θ = 1]

=RHS

Hence Proved

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