Question

If $\tan A=\frac{7}{8}$, evaluate :
(i) $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}$ (ii) ${\cot }^2\theta$

Answer 1

In △ABC△ABC

$\tan A=\frac{7}{8}$,

$\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}=\frac{1-si{n}^2\theta }{1-co{s}^2\theta }=\frac{co{s}^2\theta }{si{n}^2\theta }=co{t}^2\theta =\frac{1}{ta{n}^2\theta }=\frac{8^2}{7^2}=\frac{64}{49}$

(ii) $co{t}^2\theta =\frac{64}{49}$