Question
Prove that $\cos ^{-1} \frac{63}{65}+2 \tan ^{-1} \frac{1}{5}=\sin ^{-1} \frac{3}{5}$.
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| $X = x_i$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x_i)$ | $2k^4$ | $3k^2 - 5k^3$ | $2k - 3k^2$ | $3k - 1$ |