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Question Number 111079 by shahria14 last updated on 02/Sep/20

Answered by mr W last updated on 02/Sep/20

$$t={\cos }^{-1}\frac{5}{13}$$$$\Rightarrow \cos t=\frac{5}{13}$$$$\Rightarrow \sin t=\frac{12}{13}$$$$\tan \frac{t}{2}=\frac{\sin t}{1+\cos t}=\frac{\frac{12}{13}}{1+\frac{5}{13}}=\frac{2}{3}$$$$\Rightarrow \frac{1}{2}{\cos }^{-1}\frac{5}{13}=\frac{t}{2}={\tan }^{-1}\frac{2}{3}$$

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