If `sin theta+costheta=sqrt(2)costheta` then what is `(costheta-sintheta)` equal to ?

Options

A. `-sqrt(2)costheta`
B. `-sqrt(2)sintheta`
C. `sqrt(2)sintheta`
D. `2sin theta`

Answer

C

Explanation

`sintheta+costheta=sqrt(2)costheta` . . . (1)
Let `costheta-sintheta=p` . . . (2)
`(1)^(2)+(2)^(2)rArrsin^(2)theta+cos^(2)theta+2sinthetacostheta+cos^(2)theta+sin^(2)theta`
`-2sinthetacostheta=2cos^(2)theta+p^(2)`
`rArr2=2cos^(2)theta+p^(2)`
`rArrp^(2)=2(1-cos^(2)theta)=2sin^(2)theta`
`rArrp=sqrt(2)sintheta`