Find the value of Sin theta + Cos theta?

Given

sinθ – cosθ = 1/2

Find out

sinθ + cosθ

Solution

sinθ – cosθ = 1/2
On squaring both sides we get,
(sinθ – cosθ)² = (1/2)²
=sin²θ + cos²θ – 2 sinθcosθ = 1/4

Using the identity sin²θ + cos²θ = 1 we get
=1 – 2 sinθcosθ = 1/4
=2sinθcosθ = 1- (1/4) = 3/4

(sinθ +cosθ)² = sin²θ + cos²θ + 2 sinθcosθ
= 1 + 3/4 = 7/4
sinθ + cosθ = √(7/4) = (√7)/2

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