If `cos^(4)theta-sin^(4)theta=(2)/(3)=(2)/(3)`, then the value of `2cos^(2)theta -1` is(यदि `cos^(4)theta-sin^(4)theta=(2)/(3)=(2)/(3)` है तो `2 cos^(2) theta-1` का मान ज्ञात क्या होगा )

Options

A. 0
B. 1
C. `(2)/(3)`
D. `(3)/(2)`

Answer

c

Explanation

`cos^(4)theta-sin^(4)theta+(2)/(3)`
`[a^(4)-b^(4)=(a^(2)-b^(2))(a^(2)+b^(2)))`
`rArr1xx(cos^(2)theta-sin^(2)theta)=(2)/(3)`
`rArr1xx (cos^(2)theta-sin^(2)theta)=(2)/(5)`
`[sin^(2)theta=1-cos^(2)theta]`
`rArr 2cos^(2)theta-1=(2)/(3)`