Home
Class 12
MATHS
Solve sin^(2) theta-cos theta=1/4, 0 le ...

Solve `sin^(2) theta-cos theta=1/4, 0 le theta le 2pi`.

Text Solution

Verified by Experts

The correct Answer is:
`theta=pi/3, (5 pi)/3`
`sin^(2) theta - cos theta=1/4`
or `1-cos^(2) theta - cos theta=1/4`
or `4 cos^(2) theta+4 cos theta -3=0`
or `(2 cos theta+3) (2 cos theta-1)=0`
or `cos theta=1/2, -3/2` (rejected)
`rArr theta = pi//3, (5pi)/3` in the given interval
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.3|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 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

Solve sin^(2) theta-2 cos theta+1/4=0

Solve 3sin^2 theta -cos^2 theta=0

Solve sin 2 theta+cos theta=0 .

Solve sin^(2) theta gt cos^(2) theta .

The number of solution of sec^(2) theta + cosec^(2) theta+2 cosec^(2) theta=8, 0 le theta le pi//2 is

Solve 2 cos^(2) theta+3 sin theta=0

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

Let P (sin theta, cos theta) (0 le theta le 2pi) be a point and let OAB be a triangle with vertices (0,0) , (sqrt(3/2),0) and (0,sqrt(3/2)) Find theta if P lies inside triangle OAB

Solve 3 cos^(2) theta=sin^(2) theta