Prove the following identities:(1−sinθ )(1+sinθ ) (1−cosθ )(1+cosθ ) =tan2θ

Taking LHS=(1−sinθ )(1+sinθ ) (1−cosθ )(1+cosθ ) using identity (a2−b2)=(a+b)(a−b)=12−(sinθ ) 212−(cosθ ) 2=cos2θ sin2θ =tan2θ =RHS[∵cos2θ +sin2θ =1]

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Prove the following identities: { ( 1- { } ) ( 1+ { } )

Question

Prove the following identities:
$\frac{( 1 - cos θ ) ( 1 + cos θ )}{( 1 - sin θ ) ( 1 + sin θ )} = tan^{2} θ$

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Prove the following identities:

\frac{( 1 - cos θ ) ( 1 + cos θ )}{( 1 - sin θ ) ( 1 + sin θ )} = tan^{2} θ

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Taking

L H S = \frac{( 1 - cos θ ) ( 1 + cos θ )}{( 1 - sin θ ) ( 1 + sin θ )}

using identity

(a^{2} - b^{2}) = (a + b) (a - b)

= \frac{1 ^{2} - ( cos θ ) ^{2}}{1 ^{2} - ( sin θ ) ^{2}} = \frac{sin ^{2} θ}{cos ^{2} θ} = tan^{2} θ = R H S [∵ cos^{2} θ + sin^{2} θ = 1]

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Question Text	Prove the following identities: $\frac{( 1 - cos θ ) ( 1 + cos θ )}{( 1 - sin θ ) ( 1 + sin θ )} = tan^{2} θ$
Answer Type	Text solution:1
Upvotes	150