Question

Show that ( cosec theta - cotton theta) ^ = 1-cos theta/1+cos theta

Answer 1

Please see the attachment

Answer 2

(Cosecθ - Cotθ)² = (1 - Cosθ)/(1 + Cosθ)

Step-by-step explanation:

(cosecθ - Cotθ)² = (1 - Cosθ)/(1 + Cosθ)

LHS

= (cosecθ - Cotθ)²

Cosecθ  = 1/Sinθ

Cotθ  = Cosθ /Sinθ

= (1/Sinθ  - Cosθ /Sinθ )²

= (1 - Cosθ)²/Sin²θ

= (1 - Cosθ )(1 - Cosθ )/(1 - Cos²θ )

= (1 - Cosθ )(1 - Cosθ )/ (1 + Cosθ )(1 - Cosθ )

= (1 - Cosθ )/ (1 + Cosθ )

= RHS

QED

Proved

(Cosecθ - Cotθ)² = (1 - Cosθ)/(1 + Cosθ)

Learn more:

1/secx-tanx -1/cos = 1/cosx - 1/secx+tanx

https://brainly.in/question/8160834

Prove that: (sin3x+sinx)sinx+(cos3x-cosx)cosx=0

https://brainly.in/question/6631850