Question

how to do this... question from differentiation​

Answer 1

Answer:

let a = (1+cos x) / sin x

a² = (1+cos x)² / sin²x

a² = (1 + cos²x + 2cos x) / sin²x

a² + 1 = 1 + (1+cos²x+2cos x) / sin²x

=> (sin²x + 1 + cos²x + 2cos x) / sin²x

=> 2( 1+cos x) / sin²x

=> (1/a²+1) => sin²x / 2(1+cos x)

y = tan⁻¹a

dy/da = 1/a² + 1

=> dy/dx = 1/2 [ sin²x /1+cos x ]