# If Sin Θ – Cos Θ = ½ Then Find the Value of Sin Θ + Cos Θ

By BYJU'S Exam Prep

Updated on: September 25th, 2023

If sin θ – cos θ = ½ then the value of sin θ + cos θ is √7/2

We have to find the value of the given expression.

Given that sin θ – cos θ = ½

Now to find sin θ + cos θ

On squaring both sides of the given equation we get,

(sin θ – cos θ)2 = (½)2

sin2 θ + cos2 θ – 2 sin θ cos θ = ¼

1 – 2 sin θ cos θ = ¼ [As sin2 θ + cos2 θ = 1]

2 sin θ cos θ = 1 – ¼

On simplifying we get

2 sin θ cos θ = ¾

Now, on squaring the expression sin θ + cos θ we get

(sin θ + cos θ)2 = sin2 θ + cos2 θ + 2 sin θ cos θ

sin θ + cos θ = √sin2 θ + cos2 θ + 2 sin θ cos θ

sin θ + cos θ = √1 + 2 sin θ cos θ

As we know that sin2 θ + cos2 θ = 1

sin θ + cos θ = √1 + ¾

sin θ + cos θ = √7/4

On simplifying we get

sin θ + cos θ = √7/2

### Trigonometry

Trigonometry is one of the most important branches of mathematics and has a wide range of applications. The study of the relationships between the sides and angles of right triangles is essentially central to the branch of mathematics known as rigonometry. Therefore, trigonometric formulas, functions, or trigonometric identities can help you identify missing or unknown angles or sides in right triangles. Trigonometry angles can be expressed in degrees or radians.

Summary:-

## If Sin Θ – Cos Θ = ½ Then Find the Value of Sin Θ + Cos Θ

If sin θ – cos θ = ½ then the value of sin θ + cos θ is √7/2. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle.

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