If $ \tan \theta = \large\frac{20}{21}$ then $ \large\frac{\cos \theta - \sin \theta}{\cos \theta +\sin \theta}$

Question

$\begin{array}{1 1}(A) \; \large\frac{1}{41} \\(B)\;\large\frac{1}{20} \\(C)\;\large\frac{1}{21} \\(D)\; \large\frac{1}{20} \end{array}$

Answer 1

Solution :

Given :$\tan \theta = \large\frac{20}{21} $

Dividing all terms of $\large\frac{\cos \theta - \sin \theta }{\cos \theta +\sin \theta}$ by $\cos \theta$

$\qquad=\large\frac{1- \tan \theta}{1+\tan \theta }$

$\qquad= \large\frac{1- \Large\frac{20}{21}}{1+\Large\frac{20}{21}}$

$\qquad= \large\frac{21-20}{21+20}$

$\qquad= \large\frac{1}{41}$