Question

if cosec theta + cot theta = p, then find cos theta = p^2 - 1/ p^2 + 1​

Answer 1

Answer:

Step-by-step explanation:

cosecθ + cotθ = p

1/sinθ  + cosθ/sinθ = p

1+cosθ = psinθ

Squaring both the sides

(1+cosθ)² = p² (sin²θ)

(1+cosθ)² = p² (1-(cosθ)²)

(1+cosθ)² = p² (1-(cosθ)) (1+cosθ)

1+cosθ = p² (1-cosθ)

1 + cosθ = p² - p²cosθ

cosθ+p²cosθ = p² - 1

cosθ(p² + 1) = p² -  1

cosθ = (p²- 1)/(p² + 1)

Hence proved.