If `cos_(theta)+sin_(theta)=sqrt2` then `cos_(theta)-sin_(theta)` is(यदि`cos_(theta)+sin_(theta)=sqrt2` है तो `cos_(theta)-sin_(theta)`)

Options

A. `sqrt2 tan theta`
B. `-sqrt2 cos theta`
C. `-sqrt2 sin theta`
D. `-sqrt2 sin`

Answer

d

Explanation

`sin theta-cos theta=(1)/(2)` ......(i)
`rArr sin theta++cos theta=m` (ii)
then,
`a^(2)+b^(2)=c^(2)+d^(2)`
`1^(@)+1^(2)=((1)/(2))^(2)+m^(2)`
`2=(1)/(4)+m^(2)`
`m^(2)=2-(1)/(4)=(7)/(4)`
`rArrm=sqrt(7)/(2)`