Question

d Exam
prove
that
&
tan theta/
1-cot theta+
Cot theta/1-tan theta= 1 +tan theta+ cot theta​

Answer 1

Answer:

LHS

= tan A / 1-cot A + cot A/1-tan A

= tan^2 A/tan A - 1 - cot A/tan A - 1

= tan^3-1/tan A ( tan A-1)

= (tan^2 + 1 + tan A)/tan A

= sec^2 A + tan A / tan A

= 1 + 1/cos^2 A / sin A/ cos A

= 1+ 1/sin A cos A = 1+ sec A cosec A

Now,

RHS

= 1+ tan A + cot A

= 1 + sin A/cos A + cos A / sin A

= 1+ sin^2 A + cos^2 A / sin A cos A

= 1+ 1/sin A cos A

= 1 + sec A cosec A

Therefore,

LHS = RHS

Hence proved the required identity.

Hope this helps you !