Question

Sinα*cosα , если sinα-cosα=√2

Answer 1

$Sin \alpha -Cos \alpha = \sqrt{2}\\\\(Sin \alpha -Cos \alpha ) ^{2} =( \sqrt{2} ) ^{2}\\\\Sin ^{2} \alpha -2Sin \alpha Cos \alpha +Cos ^{2} \alpha =2 \\\\1-2Sin \alpha Cos \alpha =2\\\\2Sin \alpha Cos \alpha =-1\\\\Sin \alpha Cos \alpha =- \frac{1}{2}$

Answer 2

To find the value of sinα * cosα, we first need to determine the values of sinα and cosα.

Given the equation sinα - cosα = √2, we can use trigonometric identities to solve for sinα and cosα.

Step 1: Square the given equation.

(sinα - cosα)^2 = (√2)^2

sin^2α - 2sinαcosα + cos^2α = 2

Step 2: Use the trigonometric identity sin^2θ + cos^2θ = 1.

1 - 2sinαcosα = 2

Step 3: Isolate the term with sinαcosα.

2sinαcosα = 1 - 2

Step 4: Divide by 2.

sinαcosα = -1/2

So, sinα * cosα = -1/2.