Question

Evaluate sinA•cosA, if sinA + cosA=√2​

Answer 1

Step-by-step explanation:

(sinA+cosA)²=(√2)²

sin²A+cos²A+2sinA.cosA=2

1+2sinA.cosA=2

2sinA.cosA=2-1

sinA.cosA=1/2

Answer 2

Answer:

The answer to this question is 1/2

Step-by-step explanation:

Given that, sinA+cosA = $\sqrt{2}$

Now in order to generate an expression like (sinA.cosA) we are squaring the equation

On squaring both sides of the equation we get,

(sinA+cosA)² = ($\sqrt{2}$)²

or, sin²A + cos²A + 2.sinA.cosA = 2              ( ∵ (a+b)² = a²+b²+2ab)

or, 2sinA.cosA = 2-1          ( ∵  sin²A + cos²A = 1   )

or, 2sinA.cosA = 1

or, sinA.cosA = 1/2