Home
Class 12
MATHS
The number of solutions of the pair of e...

The number of solutions of the pair of equations `2s in^2theta-cos2theta=0` `2cos^2theta-3sintheta=0` in the interval `[0,2pi]` is

A

zero

B

one

C

two

D

four

Text Solution

Verified by Experts

The correct Answer is:
C
`2sin^(2)theta-cos2theta=0rArr2sin^(2)theta-(1-2sin^(2)theta)=0`
`rArrsin^(2)theta=(1)/(4)`
`rArrsintheta=+-(1)/(2)` …(i)
Also, `2cos^(2)theta=3sinthetarArr2sin^(2)theta+3sintheta-2=0`
`rArr(sintheta+2)(2sintheta+1)=0`
`rArrsintheta=(1)/(2)` ...(ii)
From Eqs . (i0 and (ii), `sintheta=(1)/(2)`
Two solutions exist in `[0,2pi]`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of solutions of the pair of equations 2sin^(2)theta-cos(2 theta)=0,2cos^(2)theta-3sin theta=0 in the interval [0,2 pi] is

The number of solution of the pair of equations 2sin^(2)theta-cos2 theta=0and2cos^(2)theta-3sin theta=0 in the interval [0,2 pi] is 0 (b) 1 (c) 2 (d) 4

The number of solutions of equations 3cos2theta+5costheta =1 in [0,2pi] is

The number of solutions of equation 3cos2 theta+5cos theta=1 in [0,2 pi] is

Statement-1: The number of solutions of the simultaneous system of equations 2"sin"^(2)theta-"cos" 2 theta =0 2"cos"^(2)theta - 3"sin" theta = 0" in the interval "[0, 2pi] is two. Statement-2: If 2"cos"^(2)theta-3"sin" theta = 0, "then" theta does not lie in in III or IV quadrant.

The number of solutions of the equation (log_(2)cos theta)^(2)+log.(4)/(cos theta) (16 cos theta)=2 in the interval [0, 2pi) is

The number of solution of the equation sin theta cos theta cos 2 theta .cos 4theta =1/2 in the interval [0,pi]