Question

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

Answer 1

Answer with Step-by-step explanation:

Given :  (cosecA – sinA)(secA – cosA)(tanA + cotA) = 1

L.H.S = (cosecA – sinA)(secA – cosA)(tanA + cotA)

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

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

= (1 − sin²A/sinA) ×  (1 − cos²A/cosA) × (sin²A + cos²A/sinA×cosA)

= (cos ²A/sinA) (sin²A/cosA) (1/sinA cosA)

[By using the identity, (1 - sin²θ) = cos²θ,(1− cos²θ = sin²θ & sin² θ + cos² θ = 1]

= (cos²A × sin²A)/(sin²A cos²A)

= 1

L.H.S = R.H.S  

Hence Proved..

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Answer 2

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