(D) Given expression: $(1-\cos \theta)(1+\cos \theta)$.Using the algebraic identity $(a-b)(a+b) = a^2 - b^2$,we have:$(1-\cos \theta)(1+\cos \theta) =

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(D) Given expression: $(1-\cos \theta)(1+\cos \theta)$.Using the algebraic identity $(a-b)(a+b) = a^2 - b^2$,we have:$(1-\cos \theta)(1+\cos \theta) = 1^2 - \cos^2 \theta = 1 - \cos^2 \theta$.According to the fundamental trigonometric identity $\sin^2 \theta + \cos^2 \theta = 1$,we can write $1 - \cos^2 \theta = \sin^2 \theta$.Therefore,the correct option is $D$.