The number of solutions of the pair of equations `2s in^2theta-cos2theta=0` `2cos^2theta-3sintheta=0` in the interval `[0,2pi]` is 0 (b) 1 (c) 2 (d) 4

Options

A. Zero
B. one
C. two
D. four

Answer

C

Explanation

`2sin^(2)theta-cos2theta=0`
`impliessin^(2)theta=(1)/(4)impliessintheta=+-(1)/(2)" "...(i)`
Also, `" "2cos^(2)//theta=3sintheta`
`implies2sin^(2)theta+3sintheta-2=0`
`implies" "sintheta=(1)/(2)" "...(ii)`
From Eqs. (i) and (ii), `sin theta=(1)/(2)`
Two solutions exist in `[0, 2pi]`