If sin A + cos A = (√(3))/2 , find sin²A + cos²A + 2sin Acos A.

If sin A + cos A = (√(3))/2 , find sin²A + cos²A + 2sin…

If sin A + cos A = $\frac{\sqrt{3}}{2}$ , find sin²A + cos²A + 2sin Acos A.

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{3}{4}$ .

sin A + cos A = $\frac{\sqrt{3}}{2}$

⇒ (sin A + cos A)² = $\left(\frac{\sqrt{3}}{2}\right)^2$

⇒ sin²A + cos²A + 2sin Acos A = 3/4