Question

Cosec A - Cot A = Sin A / 1 + Cos A​

Answer 1

Answer:

Cosec A - Cot A = Sin A / 1 + Cos A

LHS= Cosec A - Cot A

= 1/sinA - cosA /sin A

= 1-cosA /sin A

= multiple numerator and denominator by 1+cosA

= 1-cosA /sinA × 1+cosA/1+cosA

= 1-cos²A/sinA (1 + cosA) {a²-b²= (a-b)(a+b) }

= sin²A/ sinA (1 + cosA)

= sinA /1 +cosA= RHS

hence proved