Home
Class 12
MATHS
The value of alpha such that sin^(-1)2/(...

The value of `alpha` such that `sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha` are the angles of a triangle is `(-1)/(sqrt(2))` (b) `1/2` (c) `1/(sqrt(3))` (d) `1/(sqrt(2))`

A

`(1)/(2)`

B

`(sqrt(3))/(2)`

C

`(1)/(sqrt(2))`

D

`(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
`becausesin^(-1)((2)/(sqrt(5)))+sin^(-1)((3)/(sqrt(10)))+sin^(-1)alpha=pi`
`impliestan^(-1)(2)+tan^(-1)(3)+sin^(-1)alpha=pi`
`impliespi-tan^(-1)(1)+sin^(-1)(alpha)=piimpliesalpha=(1)/(sqrt(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

sin^(-1)(1/2)-2sin^(-1)(1/(sqrt(2)))

Show that "sin"^(-1)(sqrt(3))/2+"tan"^(-1)1/(sqrt(3))=(2pi)/3

1. sin^(-1)((1)/(sqrt(2))) 2. cos^(-1)((sqrt(3))/(2))

Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)} is

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

The value of expression tan^(- 1)((sqrt(2))/2)+sin^(- 1)((sqrt(5))/5)-cos^(- 1)((sqrt(10))/10)

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

sin(A+B)=1/sqrt(2) cos(A-B)=sqrt3|2