Question

if sin theta cos theta =1/2 then find the value of (sin theta + cos theta)​

Answer 1

Given

→ sin∅ cos∅ = ½

Solution

Since we know that,

• (a + b)² = a² + b² + 2ab

→ (sin∅ + cos∅)² = sin²∅ + cos²∅ + 2 sin∅ cos∅

→ (sin∅ + cos∅)² = 1 + 2(1/2)

→ (sin∅ + cos∅)² = 1 + 1

→ (sin∅ + cos∅)² = 2

→ sin∅ + cos∅ = √2

Answer: √2

Answer 2

Answer:

√2

Step-by-step explanation:

Given :

sinθ.cosθ=1/2

multiplying by 2 on both sides

2sinθ.cosθ=1

sin2θ=1

∴ 2θ=sin⁻¹(1)

2θ=90°

θ=45°

∴sinθ+cosθ=sin45+cos45

                  =(1/√2) + (1/√2)

                  =2/√2

                =√2