Question

Prove if it's an identity
cot^2-cos^2 = (cos^2)(cot^2)

Answer 1

you need an "argument" after a trig function, something like cos^2 by itself is meaningless. You meant
cot^2 θ - cos^2 θ = (cos^2 θ)(cot^2 θ)

LS = cot^2 θ - cos^2 θ
= (cotθ + cosθ)(cotθ - cosθ)
= (cosθ/sinθ + cosθ)(cosθ/sinθ - cosθ)
= (cosθ +sinθcosθ)(cosθ - sinθcosθ)/(sin^2 θ)
= (cos^2 θ - sin^2 θ cos^2 θ)/(sin^2θ)
= cos^2 θ(1 - sin^2 θ)/sin^2 θ , but 1 - sin^2 θ = cos^2 θ
= (cos^2 θ/sin^2 θ)(cos^2 θ)
= (cot^ θ)(cos^2 θ)
= RS

Answer 2

Thank you