Question

Prove that, ( cosec A - sin A ) ( sec A - cos A ) = 1 / tan A + cot A

Answer 1

( cosec A - sin A ) ( sec A - cos A ) 
= (1/sinA - sinA) (1/cosA - cosA)
=[(1-sin²A)/sinA][ (1-cos²A)/cosA]
=(cos²A.sin²A)/(sinA.cosA)
=(cosA.sinA)/1
=(cosA.sinA)/(sin²A + cos²A)
 
dividing num. and deno by cosA.sinA

=1/[(sinA/cosA) + (cosA/sinA)]
=1/(tanA+ cotA)
proved 

Answer 2

Answer:

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