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Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$

$(a)\; \large\frac{3}{4} \qquad(b)\; \large\frac{4}{3} \qquad(c)\; \large\frac{5}{4}\qquad(d)\; \large\frac{5}{3}$

1 Answer

Let $cot^{-1}\large\frac{3}{4}$$=y$
$\Rightarrow\:coty=\large\frac{3}{4}$
$\therefore\:\:siny=\large\frac{4}{5}$
Substituting the value in the given equation we get
$cos(tan^{-1}x)=siny=\large\frac{4}{5}$
$\Rightarrow\:tan^{-1}x=cos^{-1}\large\frac{4}{5}$
Let $cos^{-1}\large\frac{4}{5}$$=a$
$\Rightarrow\:cosa=\large\frac{4}{5}$
$\Rightarrow\:tana=\large\frac{3}{4}$
Substituting the value of $a$ we get
$tan^{-1}x=a$
$\Rightarrow\: tana=x$
or
$x=\large\frac{3}{4}$
answered Mar 21, 2014 by rvidyagovindarajan_1
 
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