Question

Sin²x-1+ cos²x(1 - sin x)(1 + sin x)

Answer 1

Ответ:

Пошаговое объяснение:

$sin^2(x)-1+cos^2(x)(1-sin(x))(1+sin(x))\\-(1-sin^2(x))+cos^2(x)(1-sin^2(x))\\-cos^2(x)+cos^2(x)*cos^2(x)\\cos^2(x)(cos^2(x)-1)$

Answer 2

Let's simplify the expression step by step:

1. Start with the given expression: Sin²x - 1 + cos²x(1 - sinx)(1 + sinx)

2. Recall the trigonometric identity: sin²x + cos²x = 1. We can replace sin²x + cos²x with 1:

   1 - 1 + cos²x(1 - sinx)(1 + sinx)

3. Simplify 1 - 1, which equals 0:

   0 + cos²x(1 - sinx)(1 + sinx)

4. Now, distribute cos²x into the expression (1 - sinx)(1 + sinx):

   cos²x(1 - sin²x)

5. Use the trigonometric identity sin²x = 1 - cos²x to simplify sin²x to 1 - cos²x:

   cos²x(1 - (1 - cos²x))

6. Distribute cos²x into the expression 1 - (1 - cos²x):

   cos²x(1 - 1 + cos²x)

7. Simplify further:

   cos²x(cos²x)

8. Finally, simplify by multiplying the two cosine terms:

   cos⁴x

So, the simplified expression is cos⁴x.