Home
Class 12
MATHS
cos^(-1)((1)/(sqrt(2))(cos.(11pi)/(10)-s...

`cos^(-1)((1)/(sqrt(2))(cos.(11pi)/(10)-sin.(pi)/(10)))` is :

A

`(7pi)/(10)`

B

`(3pi)/(10)`

C

`(7pi)/(20)`

D

`(17pi)/(20)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(1)/(sqrt(2))(cos.(11pi)/(10)-sin.(pi)/(10))`
`= (1)/(sqrt(2))(cos.(9pi)/(10)-sin.(9pi)/(10))`
`= cos ((pi)/(4)+(9pi)/(10))=cos.(23pi)/(20)=cos.(17pi)/(20)`
`rArr cos^(-1)(cos((17pi)/(20)))=(17pi)/(20)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of cos^(-1){(1)/(sqrt(2))(cos((9 pi)/(10))-sin((9 pi)/(10)))}

Find the value of the following inverse trigonometric expression: cos^(-1)(1/(sqrt(2))("cos"(9pi)/10-"sin"(9pi)/10))

the value of (cos(pi))/(2^(2)),(cos(pi))/(2^(3)),(cos(pi))/(2^(4))*(cos(pi))/(2^(10))(sin(pi))/(2(10)) is (a) (1)/(1024) (b) (1)/(512) (c) (1)/(256) (d) (1)/(128)

Find the value of following expression: [(1-cos(pi)/(10)+i sin(pi)/(10))/(1-cos(pi)/(10)-i sin(pi)/(10))]^(10)

Statement-1: cos((pi)/(10))cos((2pi)/(10))cos((4pi)/(10))=(cos((8pi)/(10)))/(2^(3)sin((pi)/(10))) Statement-2: cos A.cos2A.cos2^(2)A.......cos(2^(n-1)A)=(sin(2^(n)A))/(2^(n)sinA)

cos((pi)/(7))*cos(2(pi)/(7))*cos(10(pi)/(7))-sin((pi)/(14))*sin(3( pi)/(14))*sin(5(pi)/(14)) Find value.

Which of the following is/are the value of "cos"[1/2cos^(-1)(cos(-(14pi)/5)]? cos(-(7pi)/5) (b) sin(pi/(10)) cos((2pi)/5) (d) -cos((3pi)/5)

(sin((pi)/(10))+sin(13(pi)/(10)))(cos^(2)((pi)/(6))-cos^(2)((pi)/(10))) is equal to

cos2^(3)((pi)/(10))cos2^(4)((pi)/(10))cos2^(5)((pi)/10)....cos2^(10)((pi)/10) is equal to A. (1)/(128) B (1)/(256) C (1)/(512)sin(pi)/(10) D (sqrt(5)-1)/(512)sin(3 pi)/(10)