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  • If cos into bracket sin inverse 2 divided 5 plus cos inverse x equal to 0 then x is equal to A. 1 divided 5 B. 2 divided 5 C. 0 D. 1

If \cos\left ( sin^{-1}\frac{2}{5} + cos^{-1}x \right )=0, then x is equal to

 A. \frac{1}{5}

B. \frac{2}{5}

C.0

D.1

Answers (1)

Answer: (B)

Given, \cos\left ( Sin^{-1}\frac{2}{5}+cos^{-1}x \right )=0

Let Sin^{-1}\frac{2}{5}+cos^{-1}x =\theta

So \cos \theta =0.......(1)

Principal value \cos^{-1} x is \left [ 0,\pi \right ].......(2)

Also , we know that \cos\frac{\pi}{2}=0......(3)

From (1) ,,(2), and (3) we have

\theta =\frac{\pi}{2}

But \theta =\sin^{-1}\frac{2}{5}+\cos^{-1}x

So,

\sin^{-1}\frac{2}{5}+\cos^{-1}x=\frac{\pi}{2}

We know that \sin^{-1}x+\cos^{-1}x=\frac{\pi}{2} for\: all \: x\epsilon \left [ -1 ,1\right ]

As \sin^{-1}\frac{2}{5}+\cos^{-1}x=\frac{\pi}{2}

so x=\frac{2}{5}

 

 

Posted by

infoexpert24

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