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Prove that .
Prove that $\tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$.
Given: $\frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$
To show: $\tan^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{4} - \frac{1}{2} \cos^{-1}\left(\frac{4}{5}\right)$
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From ISC 2018 Specimen Mathematics Paper 1, question 4.