Question

Cos(90- theta)÷1+sin(90-theta)+1+sin(90-theta)÷cos(90-theta)= 2 cosec theta

Answer 1

Answer:

solved

Step-by-step explanation:

Cos(90- theta)÷1+sin(90-theta)+1+sin(90-theta)÷cos(90-theta)= 2 cosec theta

let theta = ∝

Cos(90- ∝)÷1+sin(90-∝)+1+sin(90-∝)÷cos(90-∝)= 2 cosec∝

LHS = Cos(90- ∝)÷1+sin(90-∝)+1+sin(90-∝)÷cos(90-∝)

= sin∝÷1+cos∝+1+cos∝÷sin∝ = {(1+cos∝)² + sin²∝} ÷ sin∝(1+cos∝)

= {(1+2cos∝ + cos²∝ + sin²∝} ÷ sin∝(1+cos∝) = {(1+2cos∝ +1 } ÷ sin∝(1+cos∝)

= 2(1+cos∝ ) ÷ sin∝(1+cos∝) = 2/sin∝ = 2 cosec∝ = RHS