Home
Class 12
MATHS
(1 + cos"" (pi)/(8))(1 + cos"" (3pi)/(8)...

`(1 + cos"" (pi)/(8))(1 + cos"" (3pi)/(8)) (1 + cos"" (5pi)/(8))(1 + cos"" (7pi)/(8))` =

A

`(1)/(2)`

B

`cos.(pi)/(8)`

C

`(1)/(8)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Given expression = `(1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8))`
`(1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1-cos.(3pi)/(8))(1-cos.(pi)/(8))`
`=(1-cos^(2).(pi)/(8))(1-cos^(2).(3pi)/(8))`
`=(1)/(4)(2-1-cos.(pi)/(4))(2-1-cos3.(pi)/(4))`
`=(1)/(4)(1-cos.(pi)/(4))(1-cos3.(pi)/(4))`
`=(1)/(4)(1-(1)/(sqrt(2)))(1+(1)/(sqrt(2)))=(1)/(4)(1-(1)/(2))=(1)/(8)`
Promotional Banner

Similar Questions

Explore conceptually related problems

cos^2 ""(pi)/(8) + cos ^2 ""(3 pi)/(8) + cos ^2 ""(5 pi)/(8) + cos ^2 ""(7 pi)/(8) is

Show that cos (pi)/(15) cos""(2pi)/(15) cos"" (3pi)/(15) cos"" (4pi)/(15) cos"" (5pi)/(15) cos"" (6pi)/(15) cos"" (7pi)/(15) = (1)/(128) .

Find the value of ((1 + sin"" (pi)/(10) + i cos"" (pi)/(10))/(1 + sin"" (pi)/(10) - i cos"" (pi)/(10)))^(10) .

Prove that 32 (sqrt(3)) sin"" (pi)/(48) cos"" (pi)/(48) cos"" (pi)/(24) cos"" (pi)/(12) cos"" (pi)/(6) = 3

The equation x^3=3/4x=-(sqrt(3))/8 is satisfied by x=cos((5pi)/(18)) (b) x=cos((7pi)/(18)) x=cos((23pi)/(18)) (d) x=cos((17pi)/(18))

Prove that cos^(2)""pi/8+cos^(2) ""(3pi)/(8)+cos^(2)""(5pi)/(8)+cos^(2)""(7pi)/(8)=2

The value of cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11), is

Find the value of sin^(-1) ( sin "" (5pi)/(9 ) cos "" (pi)/(9) + cos ""(5 pi )/(9) sin ""(pi) /(9))

Prove that 2 cos""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/(13)=0