Question

solve it or prove it question

Answer 1

Hey !!!

from LHS

=cosA √1 + cot²A

=cosA × √cosec²A ✔•°• cosec²A = 1 + cot²A

=cosA × cosecA

= cosA×1/sinA = cosA/sinA

=cotA

From RHS

√cosec²A - 1

we know that , cosec²A - 1 = cot²A


hence, √cosec²A - 1 = √cot²A

= cotA

So, LHS = RHS prooved here

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Hope it helps you !!!

@Rajukumar111

Answer 2

LHS:
cos A (1+cot^2A)^1/2
cos A (1+cos^2A/sin^2A)^1/2
cos A/sinA (sin^2A+cos^2A)^1/2
cot A (1)^1/2
cot A
now, taking both lhs and rhs
cot A= (cosec^2-1)^1/2

squaring both side
cot^2A=(cosec^2-1)

hence proved...
hope it will help you.