Question

Find the number of integral value of `n` so that `sinx(sinx+cosx)=n` has at least one solution.

Answer 1

`sin x(sin x+cos x)=n`
or `sin^(2) x+ sin x cos x =n`
or `(1- cos 2x)/2+(sin 2 x)/2 =n`
or `sin 2x-cos 2x=2n -1`
`rArr -sqrt(2) le 2n -1 le sqrt(2)`
or `(1-sqrt(2))/2 le n le (1+sqrt(2))/2`
or `n=0, 1`