If cosec θ = 2, show that (cot θ + sin θ/ 1 + cos θ) = 2.

Question

If cosec θ = 2, show that \((cot θ + {sin θ\over {1 + cos θ}}) = 2.\)

Answer 1

Cosec θ = 2

or 1/sinθ = 2

(cosec θ is reciprocal of sin θ)

sin θ = 1/2

which implies θ = 30 degrees.

Find the values of cos θ and cot θ at θ = 30 degrees.

cos 30° = √3/2 and cot 30° = √3

Now,

LHS = cot θ + sin θ/(1 + cos θ)

= √3 + 1/2 / (1 + √3/2)

= 2

= RHS

Hence proved.