Question #f8198

1 Answer
May 19, 2017

See Below

Explanation:

Phythagorean Identity:
sin^2(theta)+cos^2(theta)=1sin2(θ)+cos2(θ)=1
[sin^2(theta)+cos^2(theta)=1]/sin^2(theta)sin2(θ)+cos2(θ)=1sin2(θ)
cot^2(theta)+1=csc^2(theta)cot2(θ)+1=csc2(θ)

Use it to solve the identity:

1+csc^2(theta)cos^2(theta)1+csc2(θ)cos2(θ)
1+cos^2(theta)/sin^2(theta)1+cos2(θ)sin2(θ)
1+cot^2(theta)1+cot2(θ)
csc^2(theta)=RHScsc2(θ)=RHS

QED