Q. 113.8( 5 Votes )

# Prove the followings identities:

(1 + cos θ)(1 – cos θ) = sin^{2}θ

Answer :

Taking LHS =(1 – cosθ)(1+ cosθ)

Using identity , (a + b) (a – b) = (a^{2} – b^{2}) , we get

= (1)^{2} – (cosθ)^{2}

= 1 – cos^{2} θ

= sin^{2} θ [∵ cos^{2} θ + sin^{2} θ = 1]

= RHS

Hence Proved

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