If Sin ^{-1}x=\frac{\pi}{5}   for some   x\epsilon \left ( -1,1 \right )   then value of  cos^{-1}x\, \, is

  • Option 1)

    \frac{3\pi}{10}

  • Option 2)

    \frac{5\pi}{10}

  • Option 3)

    \frac{7\pi}{10}

  • Option 4)

    \frac{9\pi}{10}

 

Answers (1)

As we learnt in 

Important Results of Inverse Trigonometric Functions -

\sin ^{-1}x + \cos ^{-1}x = \frac{\pi }{2}

- wherein

When \left | x \right |\leqslant 1

 

 sin^{-1}x\:=\:\frac{\pi }{5}

cos^{-1}x\:+\:sin^{-1}x=\frac{\pi}{2}

\therefore cos^{-1}x\:=\:\frac{\pi}{2} - \frac{\pi}{5}\:=\: \frac{3 \pi}{10}


Option 1)

\frac{3\pi}{10}

Correct

Option 2)

\frac{5\pi}{10}

Incorrect

Option 3)

\frac{7\pi}{10}

Incorrect

Option 4)

\frac{9\pi}{10}

Incorrect

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