Find$$ (1 - cos^{2}\theta )(cot^{2}\theta + 1) - 1$$.
sin^2(θ)+cos^2(θ)=1
1+cot^2(θ)=cosec^2(θ)
(sin^2(θ)+cos^2(θ)=1)
(sin^2(θ)=1−cos^2(θ))
Now let's substitute:
((1−cos^2(θ))(1+cot^2(θ))-1
((sin^2(θ))(cosec^2(θ)))-1
The relationship between sin and cosec is:
cosec=1sin
thus
cosec^2(θ)=1sin^2(θ)
and so ((sin^2(θ))(1sin^2(θ)))-1=1-1 = 0
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