Question

Solve the equation for $x$: $\cos \left(\tan 1x\right)=\sin \cot -13/4.$

Answer 1

$Givencos(tan-1x)=sin(cot-134)$

$Weknowthatcos\left(x\right)=sin(\pi 2-x)$

$\Rightarrow sin(\pi 2-tan-1x)=sin(cot-134)$

$\Rightarrow \pi 2-tan-1x=cot-134$

$Weknowthat\pi 2-tan-1x=cot-1x$

$⇒cot−1x=cot−134

$\Rightarrow x=34$