Question

31. If sin theta cos theta =1/2 ,then the value of (sin theta + cos theta) is?​

Answer 1

Answer:

sinθ+cosθ=±√2

Step-by-step explanation:

Given sinθ x cosθ =1/2

Consider

(sinθ + cosθ)² it is equal to sin²θ+cos²θ+2sinθcosθ(∵(a+b)²=a²+b²+2ab)

(sinθ +cosθ)²= 1 + 2sinθcosθ (∵sin²θ+cos²θ=1)

(sinθ+cosθ)²=1 + 2 (1/2)

Therefore (sinθ+cosθ)²=2

Hence, sinθ+cosθ=±√2