Year 11 trig identity question (1 Viewer)

kpad5991 · Aug 26, 2017

prove that (1-sin^2x cos^2x)/cos^2x = tan^2x + cos^2x

-s- · Aug 26, 2017

$$\noindent$ $LHS $\equiv \frac{1-\sin^2x \cos^2x}{\cos ^2x}\\ \\ \equiv \frac{1}{\cos^2x}-\frac{\sin^2x \cos^2x}{\cos^2x} \\ \\ \equiv \sec^2 x - \sin^2x \\ \\ \equiv \tan^2x +1-\sin^2x \\ \\ \equiv \tan^2x + \cos^2x \equiv$ RHS$

split the fractions and apply the Pythagorean identity tan^2x+1=sec^2x and sin^2x+cos^2x=1

Year 11 trig identity question (1 Viewer)

kpad5991

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-s-

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