Q. 434.8( 5 Votes )

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

Answer :

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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