If `2sin^2theta-cos^2theta=2,` find the value of `theta.`

Options

A. `30^@`
B. `60^@`
C. `90^@`
D. None

Answer

C

Explanation

Given, `2sin^(2)theta-cos^(2)theta=2`
`rArr 2sin^(2)theta-(1-sin^(2)theta)=2` `[therefore sin^(2)theta+ cos^(2)theta=1]`
`rArr 2sin^(2)theta + sin^(2)theta-1=2`
`rArr 3sin^(2)theta=3`
`rArr sin^(2)theta=`
`rArr sintheta=1=sin90^(@)` `[therefore sin 90^(@)=1]`
`therefore theta=90^(@)`