Prove that { Cos(90-Theta) / 1+sin(90-Theta) } + {1+sin(90-Theta) }/ (cos(90-Theta) } =2cosec Theta - Maths - Introduction to Trigonometry

Question

Prove that { Cos(90-Theta) / 1+sin(90-Theta) } +
{1+sin(90-Theta) }/ (cos(90-Theta) } =2cosec Theta

Varun.Rawat · Accepted Answer

LHS = cos90°-θ1 + sin90°-θ + 1 +
sin90°-θcos90°-θ=sin θ1 + cos θ + 1 +
cos θsin θ=sin2θ + 1+ cos θ2sin 1 + cos
θ=sin2θ + 1 +cos2θ + 2 cos θsin 1 + cos
θ=sin2θ + cos2θ + 1 + 2 cos θsin 1 + cos
θ=1 + 1 + 2 cos θsin 1 + cos θ=21 + cos θsin 1
+ cos θ=2sin θ= 2 cosec θ=RHS