Home
Class 12
MATHS
The value of x for which "sin"(cot^(-1)(...

The value of `x` for which `"sin"(cot^(-1)(1+x))="cos"(tan^(-1)x)` is (a)`1/2` (b) 1 (c) 0 (d) `-1/2`

A

` (1)/(2)`

B

` 1`

C

`0`

D

`- (1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, ` sin [ cot ^(-1) ( 1+ x ) ] = cos ( tan ^(-1)x)" "`…(i)
and we know that,
`cot^(-1) theta = sin ^(-1)((1)/( sqrt ( 1+ theta ^(2)))) and tan ^(-1) theta = cos ^(-1)((1 )/( sqrt (1 + theta ^(2))))`
From Eq. (i),
` sin ( sin ^(-1) ""(1)/( sqrt (1+ (1 + x ) ^(2)))) = cos( cos ^(-1)""(1)/(sqrt ( 1+ x ^(2))))`
`rArr " " (1)/( sqrt (1 +( 1 + x ) ^(2)) = (1)/( sqrt (1 + x ^(2))`
`rArr " " 1+ x ^(2) + 2x + 1 = x ^(2) + 1 `
`rArr " " x = -(1)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of integer values of k for which the equation sin^(-1)x+tan^(-1)x=2k+1 has a solution is (a)1 (b) 2 (c) 3 (d) 4

Evaluate : sin (tan^(-1) x + cot^(-1) x )

The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi/2 is 2 (b) 3 (c) 1 (d) 0

Find the value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

The value of lim_(xto(1)/(sqrt(2))) (x-cos(sin^(-1)x))/(1-tan(sin^(-1)x))" is "

The value of lim_(x->1)(1-sqrt(x))/((cos^(-1)x)^2) is 4 (b) 1/2 (c) 2 (d) 1/4

Find the value of sin^(-1)x+sin^(-1)1/x+cos^(-1)x+cos^(-1)1/xdot

The value of int_(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is____.

solve for x : tan (cos^(-1) x ) = sin (cot^(-1) ""1/2)

The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x is 0 (b) 1 (c) 2 (d) 3