Home
Class 12
MATHS
The equation sin^-1x-cos^-1x=cos^-1(sqrt...

The equation `sin^-1x-cos^-1x=cos^-1(sqrt3/2)` has

A

no solution

B

unique solution

C

infinite number of solutions

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `sin^(-1)x-cos^(-1)x=cos^(-1)((sqrt(3))/(2))`
`rArrsin^(-1)x-cos^(-1)x=(pi)/(6)` …(i)
But `sin^(-1)x+cos^(-1)x=(pi)/(2)` …(ii)
On solving Eqs . (i) and (ii) , we get
`sin^(-1)x=(pi)/(3)andcos^(-1)x=(pi)/(6)`
`rArrx=(sqrt(3))/(2)` is the unique solution.
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation sin^(-1)x-cos^(-1)x=cos^(-1)((sqrt(3))/(2)) has

Solve sin^(-1) x - cos^(-1) x = cos ^(-1). sqrt3/2 .

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

Which of the following is the solution set of the equation sin^(-1)x=cos^(-1)x+sin^(-1)(3x-2)

Which of the following is the solution set of the equations sin^(-1) x = cos^(-1) x + sin^(-1) ( 3x -2) ?

The equation sqrt(3)sin x+cos x=4 has