Solve the following equation for x: ( ^ -1 x) = sin ( ^ -1 3 4 ) - Vidyadip

Question

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

✓

Answer

$\cos (\tan^{–1} x) = sin (\cot^{-1}\frac{3}{4})$
$\Rightarrow\ \ \cos\Big(\cos^{-1}\frac{1}{\sqrt{1+\text{x}^2}}\Big)$
$=\sin\Big(\sin^{-1}\frac{4}{5}\Big)$
$\Rightarrow\ \frac{1}{\sqrt{1+\text{x}^2}}=\frac{4}{5}$
$\Rightarrow\ \text{x}=\pm\frac{3}{4}$

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