Question

(Cosec theta +cot theta )square =1+cos theta/1-cos theta
(Please give th photo solution )​

Answer 1

here is the proof pls check it

Answer 2

Step-by-step explanation:

Given;

(Cosec θ +cot θ )^2 = (1+cos θ)/(1-cos θ)

For the sake of simplicity, let's consider RHS;

LHS = (1+cos θ)/(1-cos θ)

Multiply (1+cos θ)/(1+cos θ) in RHS;

= (1+cos θ)/(1-cos θ) × (1+cos θ)/(1+cos θ)

= (1+cos θ)^2/ (1-cos^2 θ)

= (1+cos θ)^2/ sin^2 θ. (1-cos^2 θ = sin^2 θ)

= (1 + cos^2 θ + 2cos θ)/sin^2 θ

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

= cosec^2 θ + cot^2 θ + 2(cos θ/sin θ)(1/sin θ) (1/sin θ = cosec θ and cos θ/sin θ = cot θ)

= cosec^2 θ + cot^2 θ + 2(cot θ)(cosec θ)

= (cosec θ + cot θ)^2

Thus, LHS = RHS.

That's all.