Question

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

• A. $\left(i\right)\frac{44}{57}\left(ii\right)\frac{21}{29}$
• B. $\left(i\right)\frac{23}{34}\left(ii\right)\frac{19}{36}$
• C. $\left(i\right)\frac{49}{64}\left(ii\right)\frac{49}{64}$
• D. None of these

Answer 1

Answer: (C)

$\left(i\right)\frac{49}{64}\left(ii\right)\frac{49}{64}$

$\cot \theta =\frac{7}{8}$
1) $\frac{(1+\sin \theta )(1-\sin \theta )}{(1+\cos \theta )(1-\cos \theta )}=\frac{1-{\sin }^2\theta }{1-{\cos }^2\theta }$
$=\frac{{\cos }^2\theta }{{\sin }^2\theta }[\because {\sin }^2\theta +{\cos }^2\theta =1]$
$={\cot }^2\theta$
$={\left[\frac{7}{8}\right]}^2=\frac{49}{64}$
2) ${\cot }^2\theta ={\left[\frac{7}{8}\right]}^2=\frac{49}{64}$