Prove that: sinθsin(90∘-θ)cot(90∘-θ)=1-sin2θ - Mathematics

Prove that:

`(sinthetasin(90^circ - theta))/cot(90^circ - theta) = 1 - sin^2theta`

Sum

L.H.S. = `(sinthetasin(90^@-theta))/cot(90^@-theta)`

= `(sinthetacostheta)/tantheta`

= `(sinthetacostheta)/(sintheta/costheta)`

= cos²θ

= 1 – sin²θ = R.H.S.

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