Verified answer

1 + cot^2 x = csc^2 x

1 / (1 + cot^2 x) = sin^2 x

(tan^2 x) / (tan^2 x + 1) = sin^2 x

sqrt(tan^2 x) / sqrt(1 + tan^2 x) = sin x

solve for tan^2 (θ) first

cos θ = sqrt (1/((tan^2 θ) +1))

cos^2 θ = 1/((tan^2 θ) +1)

((tan^2 θ) +1)= 1/cos^2 θ

(tan^2 θ)=(1-cos^2 θ)/cos^2 θ

keep in mind (tan^2 θ)=sin^2 θ/ cos^2 θ

sin^2 θ/ cos^2 θ = (1-cos^2 θ)/cos^2 θ

sin^2 θ=(1-cos^2 θ)

This is a Pythagorean Identity which u can find in Trigonometry

sin^2 θ=(1-cos^2 θ)