Question

Prove the following trigonometric identities. (1 + tan²θ) (1 − sinθ) (1 + sinθ) = 1

Answer 1

( 1 + tan²thetha) ( 1 - sin²thetha)

sec²thetha * Cos² thetha

= 1 Answer.....

Answer 2

Answer with Step-by-step explanation:

Given : (1 + tan²θ)(1 – sin θ)(1 + sin θ) = 1

L.H.S = (1 + tan²θ)(1 – sin θ)(1 + sin θ)

 = (1 + tan²θ)( (1 – sin²θ)

[By using the identity, (a + b)(a – b) = a² – b²]

= sec²θ × cos²θ

[By using the identity, (1- sin²θ) = cos²θ & 1 + tan²θ = sec²θ]

= (1/cos²θ) × cos²θ

[By using the identity, secθ = 1/ cosθ]

= 1

L.H.S = R.H.S  

Hence Proved..

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