Question

tan-1(1/2)=π\4-1/2 cos-1(4/5)
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Answer 1

$\tan^{ - 1} ( \frac{1}{2} ) = \frac{\pi}{4} - ( \frac{1}{2} \cos ^{ - 1} ( \frac{4}{5} ) )$

We know that;

$\cos ^{ - 1} ( \frac{4}{5} ) = 37 \degree$

$\tan^{ - 1} ( \frac{1}{2} ) = \frac{180 \degree}{4} - ( \frac{1}{2} \times 37 \degree)$

$\tan^{ - 1} ( \frac{1}{2} ) = 45 \degree - 18.5 \degree$

$\tan^{ - 1} ( \frac{1}{2} ) = 26.5 \degree$

But we also know that;

$\tan^{ - 1} ( \frac{1}{2} ) = 26.5 \degree$

Therefore,

LHS=RHS

HOPE THAT HELPS!!