If sin θ - cos θ = 1/5 , then find the value of sin θ + cos θ.

If sin θ - cos θ = 1/5 , then find the value of sin θ +…

If sin θ - cos θ = $\frac 1 5$ , then find the value of sin θ + cos θ.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac 7 5$ .

Given that

If sin θ - cos θ = $\frac 1 5$ ,

Sqaure both sides

⇒ sin² θ + cos² θ - 2sin θcos θ = 1/25

⇒ 1 - 2sin θcos θ = 1/25

⇒ 2sin θcos θ = 1 - 1/25 = 24/25

As we know,

⇒ (sin θ + cos θ)² = sin² θ + cos² θ + 2sin θcos θ = 1 + 24/25 = 49/25

⇒ sin θ + cos θ = 7/5