If `theta "is theta " and (cos^(2)theta)/(cot^(2) theta -cos^(2) theta) =3` then ` theta` is equal to

Options

A. `60^(@)`
B. `30^(@)`
C. `90^(@)`
D. none of these

Answer

A

Explanation

We have, ` (cos^(2) theta)/( cot^(2) theta - cos^(2) theta) = 3`
` Rightarrow cos^(2) theta = 3( cot^(2) theta - cos^(2) theta)`
` cos^(2) theta = 3 cot^(2) theta -3cos^(2) theta `
` sin^(2) theta = 3/4 Rightarrow sin theta = sqrt3/2`
` theta = 60^(@)`