Consider the following statements:
1 `f(theta) =2` has no solution
2 `f(theta) =7/2` has a solution
which of the above statement is/are correct ?

Options

A. I only
B. 2 only
C. both l and 2
D. neither 1 nor 2

Answer

B

Explanation

`f(theta) =2`
`4(1-1/4 sin^(2) 2theta=2/4 rarr 1/4 sin^(2) 2theta =+1/2-1)`
`rarr -1/4 sin^(2) 2theta =-1/2 rarr sin^(2) 2 theta =2`
`rarr sin 2 theta = pm sqrt(2)`
Hence `f(theta) =2` has no solution
`f(theta)=7/2`
`rarr-1/4 sin^(2)2theta =-1/8 rarr sin 2 theta = pm (pi)/(4)`
`rarr sin 2theta =sin (pm (pi)//4) rarr 2theta = pm (pi)//4)`
Hence `f(theta)=7/2` has a solution