Home
Class 12
MATHS
cos^(-1)((-1)/(2))-2sin^(-1)((1)/(2))+3c...

`cos^(-1)((-1)/(2))-2sin^(-1)((1)/(2))+3cos^(-1)((-1)/(sqrt(2)))-4tan^(-1)(-1)` equals to

A

`(19pi)/(12)`

B

`(35pi)/(12)`

C

`(47pi)/(12)`

D

`(43pi)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos^(-1)(-(1)/(2))-2sin^(-1)((1)/(2))+3cos^(-1)(-(1)/(sqrt(2)))-4tan^(-1)(-1)`
`=pi-cos^(-1)((1)/(2))-2((pi)/(6))+3[pi-cos^(-1)((1)/(sqrt(2)))]+4tan^(-1)(1)`
`=pi-(pi)/(3)-(pi)/(3)+3(pi-(pi)/(4))+4*(pi)/(4)`
`=(pi)/(2)+3*(3pi)/(4)+pi=(43pi)/(12)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of cos^(-1)(1/2)-2 sin^(-1)(1/2)+3cos^(-1)((-1)/(sqrt(2)))-4 tan^(-1)(-1) is equal to

tan(1)+cos^(-1)(-(1)/(2))+sin^(-1)(-(1)/(2))

sin^(-1)(1/2)+cos^(-1)(-sqrt3/2)=?

Find the values of : (1) cos^(-1)((1)/(2))+tan^(-1)((1)/sqrt(3)) (2) cos^(-1)((1)/(2))+2sin^(-1) ((1)/(2)) (3) cosec ^(-1)(-sqrt(2))+cot^(-1)(sqrt(3)) .

(a) sin^(-1)(-1/2)=? (b) cos^(-1)(sqrt3/2)=?

tan^(-1)[2cos(2sin^(-1)(1)/(2))]

Find the principal of : (1) sin ^(-1)((1)/(2)) (2) tan^(-1)(-sqrt(3)) (3) cos^(-1)(-(1)/(sqrt(2))) (4) sin^(-1)(-(1)/(2)) .