Question

Prove the following trigonometric identities. secA (1 − sinA) (secA + tanA) = 1

Answer 1

Answer with Step-by-step explanation:

Given :  secA(1 – sinA)(secA + tanA) = 1

L.H.S = secA(1 – sinA)(secA + tanA)

= 1/cosA × (1 – sinA) × (1/cosA + sinA / cosA)

[By using the identity, secA = 1/cosA and tanA = sinA/cosA]

= 1/cosA × (1 – sinA) × [(1 + sinA) / cosA]

= (1 – sinA)(1 + sinA)/cos²A

= (1 - sin²A ) / cos²A

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

= cos² A/cos2A

[By using the identity, (1 - sin²θ) = cos²θ]

= 1

secA(1 – sinA)(secA + tanA) = 1

L.H.S = R.H.S  

Hence Proved..

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Answer 2

Answer:

Refer to the attachment for your answer.