Question:
(CosecA SinA)(SecA CosA)
Answer:
Correct Question is:
Prove that (cosec A - sin A)(sec A - cos A)sec2 A = tan A
Solution:
LHS:
Given, (cosec A - sin A)(sec A - cos A)sec2 A
= (1/sin A - sin A)(1/cos A - cos A)sec2 A
= {(1 - sin2 A)/sin A}*{(1 - cos2 A)/cos A}*(1/cos2 A)
= {cos2 A/sin A}*{sin2 A)/cos A}*(1/cos2 A)
= sin A/cos A
= tan A
= RHS
So, (cosec A - sin A)(sec A - cos A)sec2 A = tan A
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