Home
Class 12
MATHS
sin (67(1)/(2))^(@)+cos(67(1)/(2))^(@) i...

`sin (67(1)/(2))^(@)+cos(67(1)/(2))^(@)` is equal to

A

`(1)/(2)sqrt(4+2sqrt(2))`

B

`(1)/(2)sqrt(4-2sqrt(2))`

C

`(1)/(4)(sqrt(4+2sqrt(2)))`

D

`(1)/(4)(sqrt(4-2sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin67(1)/(2)^(@)+cos67(1)/(2)^(@)=sqrt(1+sin135^(@))=sqrt(1+(1)/sqrt(2))` (using `cos A+sinA=sqrt(1+sin2A)`)
`=(1)/(2)sqrt(4+2sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN |Exercise Yourself|2 Videos

  • COMPOUND ANGLES

    ALLEN |Exercise EX-01|15 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    ALLEN |Exercise All Questions|1 Videos

  • DETERMINANTS

    ALLEN |Exercise All Questions|100 Videos

Similar Questions

Explore conceptually related problems

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

If |x|le1 , then 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))) is equal to _____

cos^2 48^0-sin^2 12^0 is equal to

cos 1^(@) + cos2^(@) + cos 3^(@) + ….+cos 180^(@) is equal to

If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a. 1/sqrt(5) b. 2/sqrt(5) c. 3/sqrt(5) d. sqrt(5)/3

If cos("sin"^(-1)2/5+"cos"^(-1)x)=0 , then x is equal to _____

Find all number x , y that satisfy the equation (sin^2 x +(1)/( sin^(2) x))^(2)+( cos^(2)x+(1)/(cos^(2)x))^(2)=12+(1)/(2) siny.

The value of sin\ (1/2cot^(-1)(-3/4))+cos(1/2cot^(-1)(-3/4)) is/are equal to a. 1 b. (3sqrt(2))/(10) c. sqrt(2)sin(1/2cot^(-1)(-3/4)+cot^(-1)(1))\ d. 2sin(pi-tan^(-1)(1)-1/2tan^(-1)(4/3))

sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to