if `sintheta-costheta=0,` then the value of `(sin^4theta+cos^4theta)`

Options

A. 1
B. `3/4`
C. `1/2`
D. `1/4`

Answer

C

Explanation

Given, `sintheta-costheta=0`
`rArr sintheta=costheta rArr (sintheta)/(costheta)=1`
`rArr tantheta=1` `therefore tantheta=(sintheta)/(costheta)` and `tan45^(@)=1`
`rArr tantheta=tan45^(@)`
`therefore theta=45^(@)`
Now, `sin^(4)theta+cos^(4)theta=sin^(4)45^(@)+cos^(4)45^(@)`
`=(1/sqrt(2))^(4) + (1/sqrt(2)^(4))` `[therefore sin45^(@)=cos45^(@)=1/sqrt(2)]`
`=1/4+1/4=2/4=1/2`