Question

prove the following:​

Answer 1

Step-by-step explanation:

Given :-

(Cotθ+Cosθ)/(Cotθ-Cosθ)

To find :-

Prove that (Cotθ+Cosθ)/(Cotθ-Cosθ)

= (1+Sinθ)/(1-Sinθ)

Solution :-

On taking LHS of the equation

(Cot θ + Cos θ)/( Cot θ - Cos θ)

=> [(Cos θ/Sin θ) + Cos θ] /

[(Cos θ/Sin θ) -Cos θ]

=>[(Cosθ+CosθSinθ)/Sinθ]/[(Cosθ-CosθSinθ)/Sinθ]

=> [(Cosθ+CosθSinθ)/Sinθ] /

[Sinθ/(Cosθ-CosθSinθ)]

=> (Cosθ+CosθSinθ)/(Cosθ-CosθSinθ)

=> [Cosθ(1+Sinθ)] / [Cosθ(1-Sinθ)]

=> (1+ Sin θ ) / (1 - Sin θ)

=> RHS

=> LHS = RHS

Hence, Proved.

Answer:-

(Cotθ + Cos θ )/(Cot θ-Cos θ )

= (1+ Sin θ ) / (1 - Sin θ)

Used formulae:-

→ Cot θ = Cos θ / Sin θ