Home
Class 12
MATHS
If (costheta+cos2theta)^3=cos^3theta+cos...

If `(costheta+cos2theta)^3=cos^3theta+cos^3 2theta,` then the least positive value of `theta` is equal to `pi/6` (b) `pi/4` (c) `pi/3` (d) `pi/2`

Text Solution

Verified by Experts

We have `(cos theta+ cos 2 theta)^(3)=cos^(3) theta+cos^(3) 2 theta`
i.e., `(a+b)^(3)=a^(3)+b^(3)`
`rArr ab(a+b)=0`
`rArr cos theta=0 or cos 2 theta=0 or cos theta+ cos 2 theta=0`
`rArr theta_(min)=pi/2 or theta_(min)=pi/4 or theta_(min)=pi/3`
`rArr theta_(min)=pi/4`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

If (cos theta+cos2 theta)^(3)=cos^(3)theta+cos^(3)2 theta, then the least positive value of theta is equal to (pi)/(6) (b) (pi)/(4)( c) (pi)/(3)( d) (pi)/(2)

If cos2 theta*cos3 theta*cos theta=(1)/(4) for 0

The period of cos5 theta is (a) pi^(2) (b) 2 pi (c) 2 pi/5 (d) pi/3

If sin^(22)theta+cos^(42)theta=(3)/(4) where theta in[0,(pi)/(2)] then find the sum of all values of theta (a) pi (b) -pi(c)(5 pi)/(4) (d) (pi)/(2)

If theta = pi/7 prove that cos theta* cos 2theta * cos 3theta = 1/8

If 2cos(theta)+sin(theta)=1 and (3 pi)/(2)

If theta=(2 pi)/(4033), then cos theta*cos2 theta*cos3 theta*....cos2016 theta is equal

If 2 sin(theta+(pi)/(3))=cos(theta-(pi)/(6)) , then tantheta =

For -pi/2