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The number of solutions of the equation ...

The number of solutions of the equation `cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`cos^(-1) ((1 + x^(2))/(2x)) = (pi)/(2) + (sin^(-1) x + cos^(-1) x)`
`rArr cos^(-1) ((1 + x^(2))/(2x)) = pi`
or `((1 + x^(2))/(2x)) = cos pi = -1`
or `x^(2) + 1 + 2x = 0`
or `x = -1`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
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  3. The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1...

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  12. The solution set of the equation sin^(-1)sqrt(1-x^2)+cos^(-1)x=cot^(-1...

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  17. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

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  19. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

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