Question

Упростите выражения sin^2a+cos^4a-sin^4a (^-степень) Sin^4a+sin^2acos^2a

Answer 1

$sin^2a+cos^4a-sin^4a=sin^2a+(cos^2a-sin^2a)(cos^2a+sin^2a)=\\=sin^2a+cos^2a-sin^2a=cos^2a\\\\sin^4a+sin^2acos^2a=sin^4a+sin^2a(1-sin^2a)=\\=sin^4a+sin^2a-sin^4a=sin^2a$

Answer 2

I can help you with math problems. To simplify the expression, you need to use the following trigonometric identities:

$$\sin^2 x + \cos^2 x = 1$$ $$\sin^2 x = 1 - \cos^2 x$$ $$\cos^2 x = 1 - \sin^2 x$$

Using these identities, you can rewrite the expression as:

$$\sin^2 a \cos^4 a - \sin^4 a + \sin^4 a \sin^2 a \cos^2 a$$ $$= \sin^2 a (1 - \sin^2 a)^2 - \sin^4 a + \sin^6 a (1 - \sin^2 a)$$ $$= \sin^2 a (1 - 2 \sin^2 a + \sin^4 a) - \sin^4 a + \sin^6 a - \sin^8 a$$ $$= \sin^2 a - 2 \sin^4 a + \sin^6 a - \sin^4 a + \sin^6 a - \sin^8 a$$ $$= - 3 \sin^4 a + 2 \sin^6 a - \sin^8 a$$

Therefore, the simplified expression is:

$$- 3 \sin^4 a + 2 \sin^6 a - \sin^8 a$$

I hope this helps. If you have any other math questions, feel free to ask me.Ответь+подробно.+Упростите+выражения++sin^2a+cos^4a-sin^4a+(^-степень)+Sin^4a+sin^2acos^2a