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  • If    <img alt="\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13," src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csin%20%5E%7

If    \sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13,   { then } \sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)  is equal to

Option: 1

16


Option: 2

0


Option: 3

\pi


Option: 4

16-5\pi16-5\pi


Answers (1)

best_answer

\begin{aligned} & \sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13 \\ & \sin ^{-1} \frac{\alpha}{17}=\tan ^{-1} \frac{77}{36}-\tan ^{-1} \frac{3}{4} \\ & \end{aligned}

\begin{aligned} & =\tan ^{-1}\left(\frac{\frac{77}{36}-\frac{3}{4}}{1+\frac{77}{36} \cdot \frac{3}{4}}\right) \end{aligned}

\begin{aligned} & \sin ^{-1} \frac{\alpha}{17}=\tan ^{-1}\left(\frac{8}{15}\right)=\sin ^{-1}\left(\frac{8}{17}\right) \\ & \frac{\alpha}{17}=\frac{8}{17} \\ & \alpha=8 \\ & \sin ^{-1}(\sin 8)+\cos ^{-1}(\cos 8) \\ & =3 \pi-8+8-2 \pi \\ & =\pi \end{aligned}

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Rishabh

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