Question

If `sin theta - cos theta = 1/2`, what is the value of `sin theta + cos theta`?

Answer 1

`sin t + cos t = +- sqrt7/2`

Explanation:

`(sin t - cos t)^2 = 1 - 2sin t.cos t`
`(sin t + cos t)^2 = 1 + 2sin t.cos t`
Add up the 2 equations:
`(sin t - cos t)^2 + (sin t + cos t)^2 = 2`
From given data -->
`(sin t - cos t)^2 = (1/2)^2 = 1/4`
Therefore:
`(sin t + cos t)^2 = 2 - 1/4 = 7/4`
`(sin t + cos t) = +- sqrt7/2`