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Questions  >>  Olympiad-Math  >>  Class 10
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Q)

If $ \tan \theta = \large\frac{20}{21}$ then $ \large\frac{1-\sin \theta + \cos \theta}{1+\cos \theta +\sin \theta}$

$\begin{array}{1 1}(A) \; \large\frac{6}{7} \\(B)\;\large\frac{5}{7} \\(C)\;\large\frac{4}{7} \\(D)\; \large\frac{3}{7} \end{array}$

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Solution :
Let BC = 21k and AB = 20k
$AC= \sqrt {(20 k)^2 +(21k)^2}$
$\qquad= \sqrt{400 k^2+441k^2}$
$\qquad= \large\frac{1- \sin \theta +\cos \theta}{1+ \cos \theta +\sin \theta}$
$\qquad= \large\frac{1- \Large\frac{20 k}{29 k} +\frac{21 k}{29 k}}{1+\Large\frac{21 k}{29 k} +\frac{20k}{29k}}$
$\qquad= \large\frac{29-20+21}{2-21+20}$
$\qquad = \large\frac{50-20}{20-20}$
$\qquad=\large\frac{30}{70}$
$\qquad= \large\frac{3}{7}$
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