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

1 Answer
Jun 19, 2017

#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#