Question

.
prove that
(Cosec A-cot A)^2 = 1-cosA/1+cosA
​

Answer 1

Step-by-step explanation:

Lhs= (cosec A -cot A)²

=(1/sin A - cosA/ Sin A)²

=(1-cos A /sin A)²

=(1-cos A)²/(sin²A)

since sin²A = 1- cos²A

=(1-cos A)(1-cosA)/(1²-cos²A)

we know that

a²-b² = (a+b)(a-b)

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

=1-cos A / 1+ cos A