Question

√(1+cosA/1-cosA)=(cosec A+cotA)
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Answer 1

Answer:

LHS

=√(1+cosA/1-cosA)

=√(1+cosA)^2/(1+cosA)(1-cosA)

=√(1+cosA)^2/(1-cos^2A)

=√(1+cosA)^2/sin^2A

=(1+cosA)/sinA

=1/sinA+cosA/sinA

=cosecA+cotA

=RHS

Answer 2

Step-by-step explanation:

By Rationalisation

√(1+cosA/1-cosA) × √(1+cosA/1+cosA)

√(1+cosA)^2/ 1^2 - cos^2A. { a^2-b^2 = (a+b) (a-b) }

√ ( 1+cosA)^2 / sin^2A. { 1 - cos^2A = sin^2A}

By removing square root:-

1+cosA / sin A

It can be also written as

1/sinA + cosA/sinA

So,

cosec A + cot A {1/sinA = cosec A and cos A /sin A = cot A}

Hence Proved.