Simplify the expression G( )= [(1- ^ 2 )+(1- ^ 2 ) ]^ 2 ( ^ 2 - ^ 2 )^ 2 and show…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Simplify the expression G(θ)=[(1−sin⁡2θ)+(1−cos⁡2θ)]2(sec⁡2θ−tan⁡2θ)2G(\theta)=\frac{\bigl[(1-\sin^{2}\theta)+(1-\cos^{2}\theta)\bigr]^{2}}{(\sec^{2}\theta-\tan^{2}\theta)^{2}} and show that it equals a constant. Give complete justification for each algebraic step used.

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