Question

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Answer 1

Answer:

Write tan as Sin/Cos

And Cot as Cos/Sin.

And simplify.. You will get the answer

Answer 2

Answer:

sec A.cosec A + 1  option b

Step-by-step explanation:

tan A / (1 - cot A)  + cot A /(1-tan A)

= ( sin A/cos A )/ (1 - (cos A/ sin A))  + (cos A/sin A) / (1- (sin A/cos A))

= ( sin A/cos A )/ [(sin A - cos A)/sin A] + (cos A/sin A) / [( cos A - sin A)/cosA]

= sin² A / [ cos A(sin A - cos A) ]  + cos² A / [ sin A(cos A -  sin A) ]

= sin² A / [ cos A(sin A - cos A) ]  - cos² A / [ sin A( sin A - cos A) ]

=[1/(sin A - cos A)] *  [(sin³ A - cos³ A) / cos A.sin A ]

= [1/(sin A - cos A)] *  [ (sin A - cos A)(sin² A + sin A.cos A + cos² A)] / cos A.sin A         by formula a³-b³ = (a-b)(a²+ab+b²)

= (1+sin A.cos A) / cos A.sin A

=( 1 / cos A.sin A) + (sin A.cos A)/(cos A.sin A)

=(1/cos A)((1/sin A) + 1

= sec A.cosec A + 1