Question

If tan $x=\frac{4}{3},$ then the value of $\sqrt{\frac{(1-\sin x)(1+\sin x)}{(1+\cos x)(1-cosx)}}$ is

• A. $\frac{9}{16}$
• B. $\frac{3}{4}$
• C. $\frac{4}{3}$
• D. $\frac{16}{9}$

Answer 1

Answer: (B)

$\frac{3}{4}$

$\sqrt{\frac{(1-\sin x)(1+\sin x)}{(1+\cos x)(1-\cos x)}}$
$=\sqrt{\frac{1-{\sin }^{2}x}{1-{\cos }^{2}x}}$ ....... $(\because (a-b)(a+b)=a^2-b^2)$
$=\sqrt{\frac{{\cos }^{2}x}{{\sin }^{2}x}}$ ....... $(\because {\sin }^{2}x+{\cos }^{2}x=1)$

$=\frac{\cos x}{\sin x}$

$=\cot \theta$

$=\frac{1}{\tan \theta }$

$=\frac{1}{\frac{4}{3}}=\frac{3}{4}$