Home
Class 12
MATHS
If (sin 3theta)/(cos 2theta)lt 0, then t...

If `(sin 3theta)/(cos 2theta)lt 0`, then `theta` lies in

A

`((3pi),(8),(23pi)/(48))`

B

`((7pi)/(24),(3pi)/(8))`

C

`((13pi)/(48),(7pi)/(24))`

D

`((2pi)/(4),(7pi)/(12))`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `(sin 3theta)/(cos 2theta)lt 0`
Case I. `sin theta lt 0` and `cos 2theta gt 0`
`rArr 3theta in (pi, 2pi)` and `2theta in (-(pi)/(2),(-pi)/(2))`
`rArr theta in((pi)/(3),(2pi)/(3))` and `theta in (-(pi)/(4), (pi)/(4))`
Case II. `sin 3theta gt 0` and `cos 2 theta lt 0`
`therefore 3theta in(0, pi)` and `2theta in((pi)/(2),(3pi)/(2))`
`rArr theta in(0,(pi)/(3))` and `theta in((pi)/(4),(3pi)/(4))`
From case I and II, we have
`theta in((pi)/(4),(pi)/(3))`
Since `((13pi)/(48),(7pi)/(24))in((pi)/(4),(pi)/(3))`
`therefore theta in((13pi)/(48),(7pi)/(24))`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)

Solve sin 2 theta+cos theta=0 .

sqrt((1+ cos theta)/( 1- cos theta)) + sqrt((1- cos theta)/( 1 + cos theta )) ( 0 lt theta lt pi ) is

If u=(1+cos theta)(1+cos 2theta)-sin theta.sin 2theta, v=sin theta(1+cos 2theta)+sin 2theta(1+cos theta) , then u^(2)+v^(2)=

If cos2 theta =0 ,determine |(0,cos theta,sin theta),(cos theta ,sin theta,0),(sin theta,0,cos theta)|^(2)

If pi/2 lt theta lt 3 pi/2 then sqrt( (1-sin theta)/(1+ sin theta )) - tan theta is

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If cos theta{:((cos theta, sin theta),(-sin theta, cos theta)):}+ sin theta{:((x,-cos theta),(cos theta, x)):}=I_(2) , find x.