If `sin theta + cos theta = sqrt2`, then find the value of `theta`.

Options

A. `45^(@)`
B. `60^(@)`
C. `30^(@)`
D. `90^(@)`

Answer

A

Explanation

`:. sin theta + cos theta = sqrt(2)`
On squaring both sides, we get
` rArr sin^(2) theta + cos ^(2) theta + 2 sin theta cos theta = 2 `
`rArr 1 + sin 2 theta = 2 `
` rArr sin 2 theta = 1 = sin 90^(@)`
` :. theta = 45^(@)`