Q. 15 A4.3( 6 Votes )

Prove the following identities :

(1 – cosθ)(1+ cosθ)(1+ cot2 θ) = 1

Answer :

Taking LHS = (1 – cosθ)(1+ cosθ)(1+ cot2 θ)

Using identity , (a + b) (a – b) = (a2 – b2) in first two terms , we get


= (1)2 – (cosθ)2 (cosec2 θ) [ cot2 θ +1= cosec2 θ]


= (1 – cos2 θ) (cosec2 θ)


= (sin2 θ) (cosec2 θ) [ cos2 θ + sin2 θ = 1]



=1


= RHS


Hence Proved


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