Question

Cos^4x+sin^2xcos^2x+sin^2x

Answer 1

Ответ:

1

Объяснение:

cos⁴x+sin²xcos²x+sin²x=(cos²x)²+(1+cos2x)(1-cos2x)/4+(1-cos2x)/2=(1+cos2x)²/4+(1-cos²2x)/4+(2-2cos2x)/4=(1+2cos2x+cos²2x+1-cos²2x+2-2cos2x)/4=4/4=1

Answer 2

To simplify the expression cos^4(x) + sin^2(x)cos^2(x) + sin^2(x), you can use trigonometric identities. Here's the simplification step by step:

1. Recall the trigonometric identity: sin^2(x) + cos^2(x) = 1.

2. Substitute this identity into the expression: cos^4(x) + sin^2(x)cos^2(x) + sin^2(x) = cos^4(x) + (1 - cos^2(x))cos^2(x) + sin^2(x).

3. Expand the terms: cos^4(x) + (1 - cos^2(x))cos^2(x) + sin^2(x) = cos^4(x) + cos^2(x) - cos^4(x) + sin^2(x).

4. Simplify further by canceling out the cos^4(x) terms: cos^2(x) + sin^2(x).

5. Use the Pythagorean identity sin^2(x) + cos^2(x) = 1: 1.

So, the simplified expression is 1.