Home
Class 12
MATHS
Let f(theta)=sin theta(sin theta +sin 3 ...

Let `f(theta)=sin theta(sin theta +sin 3 theta). " Then " f(theta)`

A

` ge 0," only when " theta ge 0`

B

`le 0," for all real " theta`

C

`ge 0," for all real " theta`

D

`le 0," only when " theta le 0`

Text Solution

Verified by Experts

The correct Answer is:
C
It is given,
`f(theta)=sin theta(sin theta + sin 3 theta )`
`=(sin theta +3 sin theta -4 sin^(3) theta) sin theta`
`= (4 sin theta -4 sin^(3) theta) sin theta=sin^(2) theta (4-4 sin^(2) theta )`
` =4sin^(2) theta cos^(2) theta =(2 sin theta cos theta )^(2)`
`=(sin 2 theta)^(2) ge 0`
which is true for all `theta`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Solve sin 6 theta=sin 4 theta-sin 2 theta .

Given that f(ntheta)=(2sin2theta)/(cos2theta-cos4ntheta), and f(theta)+f(2theta)+f(3theta)++f(ntheta)=(sinlambdatheta)/(sinthetasinmutheta), then the value of mu-lambda is ______

If f(theta) = |sin theta| + |cos theta|,theta in RR, then f(theta) is in the interval

Prove: (cos^2theta)/(1-tan theta) + (sin^3 theta)/(sin theta - cos theta ) = 1 + sin theta cos theta

The value of (sin 3theta+sin 5theta+sin 7 theta+sin 9 theta)/(cos 3 theta+cos 5 theta+cos 7 theta+cos 9 theta)=……………

Show that ((cos theta - cos 3theta)(sin 8theta + sin 2 theta))/((sin 5 theta - sin theta)(cos 4 theta - cos 6 theta)) = 1

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]