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Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13...

Prove that: `sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2`

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To prove that \( \sin^{-1}\left(\frac{4}{5}\right) + \sin^{-1}\left(\frac{5}{13}\right) + \sin^{-1}\left(\frac{16}{65}\right) = \frac{\pi}{2} \), we will follow these steps: ### Step 1: Combine the first two terms We start with the left-hand side (LHS): \[ \sin^{-1}\left(\frac{4}{5}\right) + \sin^{-1}\left(\frac{5}{13}\right) \] Using the formula for the sum of inverse sines: ...
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Knowledge Check

  • sin^(-1)(4//5) + sin^(-1)(5//13) + sin^(-1)(16//65) is equal to

    A
    0
    B
    `pi//2`
    C
    `pi`
    D
    `sin^(-1)(63//65)`

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