Question

Sin^2(x)-√2sinx cosx

Answer 1

Пошаговое объяснение:

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Answer 2

To simplify the expression sin^2(x) - √2sin(x)cos(x), you can use trigonometric identities. Here's the step-by-step simplification:

1. Start with the expression: sin^2(x) - √2sin(x)cos(x)

2. Recognize that sin(2x) = 2sin(x)cos(x), so you can express √2sin(x)cos(x) as (1/√2)sin(2x):

   sin^2(x) - (1/√2)sin(2x)

3. Use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x), to rewrite sin(2x) as 2sin(x)cos(x):

   sin^2(x) - (1/√2)(2sin(x)cos(x))

4. Distribute the (1/√2) to both terms inside the parentheses:

   sin^2(x) - (√2/2)sin(x)cos(x)

5. Recognize that √2/2 is equal to 1/√2, so you can rewrite (√2/2) as (1/√2):

   sin^2(x) - (1/√2)sin(x)cos(x)

Now, you have simplified the expression to sin^2(x) - (1/√2)sin(x)cos(x).