Question

If cosec theta + cot theta =m then show (m^2+1) sin theta =2m

Answer 1

Hi...☺

Here is your answer...✌

Given that,

m = cosecθ + cotθ 

m² + 1 = (cosecθ+cotθ)² + (cosec²θ-cot²θ)

= (cosecθ+cotθ)²+(cosecθ+cotθ)(cosecθ-cotθ)

= cosecθ+cotθ (cosecθ+cotθ+cosecθ-cotθ)

= cosecθ+cotθ ( 2cosecθ )

= m × 2cosecθ

=> m² + 1 = 2m cosecθ -----(1)


Now,

To Prove : (m² + 1) sinθ =2m

Proof :

LHS

= (m² + 1) sinθ

= 2m cosecθ × sinθ __ [ from (1) ]

= 2m __ [ since, cosecθ × sinθ = 1 ]

= RHS ___ [ Proved ]