SSC CHSL 2019 PYQ — Question 68

Concept

Application

Tanθ = Sinθ/Cosθ

Cotθ = Cosθ/Sinθ

Secθ = 1/Cosθ

1- sin²θ = Cos²θ

 ((secθ+tanθ)(1-sinθ))/(cosecθ(1+cosθ)(cosecθ-cotθ))

Putting the values:

= ((1/cosθ + sinθ/cosθ)(1-sinθ))/(1/sinθ(1+cosθ)(1/sinθ - cosθ/sinθ))

= ((1+sinθ)(1-sinθ) sin²θ)/(cosθ(1+cosθ)(1-cosθ))

= ((1-sin²θ) sin²θ)/(cosθ(1-cos²θ))

= ((cos²θ) sin²θ)/(cosθ(sin²θ))

= cosθ