Question

Prove the following trigonometric identities. (secθ + cosθ) (secθ − cosθ) = tan²θ+sin²θ

Answer 1

Answer with Step-by-step explanation:

Given : (secθ +cos θ)(sec θ – cos θ) = tan²θ + sin²θ

L.H.S :  (sec θ + cos θ)(sec θ – cos θ)

= (sec²θ – cos²θ)

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

[By using the identity, sec²θ = 1 + tan²θ and cos²θ = 1 – sin² θ]

= 1 + tan² θ – (1 – sin² θ)

= 1 + tan² θ – 1 + sin² θ

= tan²  θ + sin² θ

(secθ +cos θ)(sec θ – cos θ) = tan²θ + sin²θ

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

Refer to the attachment mate..☺☺