Question

1+costeta÷sinteta -sinteta ÷1+costeta=2cotteta​

Answer 1

Step-by-step explanation:

(1+cosθ)/sinθ - sinθ/(1 + cosθ) = 2cotθ;

((1 + cosθ)^2 - sin^2θ) / (sinθ)(1 + cosθ) = 2cotθ;

(1 + cos^2θ + 2cosθ - sin^2θ) / (sinθ)(1 + cosθ) = 2cotθ; ((a+b)^2 = a^2 + b^2 + 2ab);

(1 + cos^2θ + 2cosθ - (1 - cos^2θ)) / (sinθ)(1 + cosθ) = 2cotθ; (cos^2 θ + sin^2 θ = 1);

(1 + cos^2θ + 2cosθ - 1 + cos^2θ) / (sinθ)(1 + cosθ) = 2cotθ;

(2cos^2 θ + 2 cos θ )/ (sinθ)(1 + cosθ) = 2cotθ;

2cos θ (cosθ + 1) / (sinθ)(1 + cosθ) = 2cotθ;

2cosθ / sinθ = 2cotθ;

2 (cosθ/sinθ) = 2 cot θ;

2 cotθ = 2 cot θ;

cotθ = cotθ

Thus, LHS = RHS.

That's all.