Question

it is given that if sin theta - cos theta=1/2.find sin theta + cos theta

Answer 1

Given that sin theta - cos theta = 1/2.

On squaring both sides, we get

(sin theta - cos theta)^2 = (1/2)^2

sin^2 theta + cos^2 theta - 2sinthetacostheta = 1/4

1 - 2sinthetacostheta = 1/4

- 2 sinthetacostheta = 1/4 - 1

                                 = -3/4.


2 sinthetacostheta = 3/4


We know that (sin theta + cos theta)^2 = sin^2 theta + cos^2 theta + 2sinthetacostheta

(sin theta + cos theta)^2 = 1 + 2sin theta cos theta

                                        = 1 + 3/4

                                       = 7/4


Therefore sin theta + cos theta = root 7/2.


Hope this helps!

Answer 2

we have
sin theta-cos theta =1/2
squaring
[sin theta-cos theta]square=sin square theta+cos sq theta-2 sin theta cos theta
1/4=1-2 sin theta cos theta
2 sin theta cos theta=3/4
so,
[sin theta + cos theta]whole sq=1+2 sin theta cos theta
=1+3/4
sin theta + cos theta=underroot 7/2