From 3 Maths

1)cos^3θ+cosθsin^2θ
= cosθ(cos^2θ+sin^2θ)
= cosθ

2)1+1/tan^2θ
= (tan^2θ+1)/tan^2θ
= [(sin^2θ/cos^2θ) + 1]/(sin^2θ/cos^2θ)
= [(sin^2θ + cos^2θ)/cos^2θ]/(sin^2θ/cos^2θ)
= 1/sin^2θ

3)sinθtanθ+cosθ
= (sin^2θ/cosθ) + cosθ
= (sin^2θ + cos^2θ)/cosθ
= 1/cosθ

4)1-(cosθ+sinθ)^2
= 1- (cos^2θ+sin^2θ + 2cosθsinθ)
= -2cosθsinθ

5)sin^2θ/1-sin^2θ
= sin^2θ/cos^2θ
= tan^2θ