Home
Class 12
MATHS
The expression cos 3 theta + sin 3 theta...

The expression `cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin theta- cos theta)` is positive for all `theta` in

A

`(2 n pi-(3pi)/4, 2npi+pi/4), n in Z`

B

`(2npi-pi/4, 2npi +pi/6), n in Z`

C

`(2npi-pi/3, 2npi +pi/3), n in Z`

D

`(2npi-pi/4, 2npi+(3pi)/4), n in Z`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`cos 3 theta+sin 3 theta+(2 sin 2 theta-3) (sin theta - cos theta) gt 0`
or `4(cos theta - sin theta) (cos^(2) theta+ sin theta cos theta+ sin^(2) theta-sin theta cos theta) gt 0`
or `-4sqrt(2) sin (theta - pi/4) gt 0`
or `sin (theta - pi/4) lt 0`
`rArr (2n-1) pi lt theta - pi/4 lt 2npi, n in I`
`rArr 2n pi - (3pi)/4 lt theta lt 2n pi + pi/4, n in I`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercises (Matrix Match Type)|6 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Single)|90 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

y = tan theta ( sin theta + cos theta)

If cos 3theta+sin3theta+(2sin2theta-3)(sin theta-cos theta)gt0 , then theta lies in

Knowledge Check

  • the solution of sin ^3 theta cos theta - sin theta cos^3 theta = 1/4 is

    A
    `((n pi)/(4)) +(-1)^n ((pi)/(8))`
    B
    `((n pi )/(2)) +-( (pi)/(8))`
    C
    `((npi)/(4))+ (-1)^(n+1) ((pi)/(8))`
    D
    `((n pi)/(8))+(-1) ^n ((pi)/(8))`

    • Similar Questions

    Explore conceptually related problems

    determinant |"cos theta sin theta -sin theta cos theta

    Evaluate : |(cos theta, sin theta),(-sin theta,cos theta)|

    Solve (3 sin theta-sin 3 theta)/(sin theta)+(cos 3 theta)/(cos theta)=1 .

    Solve : 3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0 .

    Solve the equations: sin 2theta - cos 2 theta - sin theta + cos theta = 0

    Solve sin 3 theta-sin theta=4 cos^(2) theta-2 .

    Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

    Home
    Profile