Question

Prove:

(cos^2)θ=((cot^2)θ)/(1+(cot^2)θ)

Answer 1

@Owen17, good?

Answer 2

\[Cos^2x=\frac{Cot^2x}{1+Cot^2x}\]\[Cos^2x=\frac{Cot^2x}{Csc^2x}\]\[Cos^2x=\frac{Cos^2x/Sin^2x}{1/Sin^2x}\]\[Cos^2x=\frac{Cos^2x}{1}\]\[Cos^2x=Cos^2x\]

Answer 3

Identities used:
\[Cot^2x+1=Csc^2x\]\[Cot^2x=Cos^2x/Sin^2x\]\[Csc^2x=1/Sin^2x\]\[\frac{a}{b} \div \frac{c}{d} =\frac{a}{b} \times \frac{d}{c}\]

Answer 4

Perfect, thank you very much for your help.

Answer 5

Anytime!