Question

Sin^2альфа+sin^2альфа Cos^2альфа+ Cos^4 альфа

Answer 1

Используя основное тригонометрическое тождество  $sin^2+cos^2x=1$получим

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

Answer 2

To simplify the expression, let's work with the symbols more commonly used in mathematics:

Let α be the angle.

The expression you provided is:

sin^2(α) + sin^2(α) cos^2(α) + cos^4(α)

To simplify it, we can factor out sin^2(α):

sin^2(α) (1 + cos^2(α)) + cos^4(α)

We know that 1 + cos^2(α) is equal to sin^2(α):

sin^2(α) + cos^4(α)

Now, we can use the trigonometric identity: sin^2(α) + cos^2(α) = 1

sin^2(α) + cos^2(α) = 1

Therefore, cos^4(α) = (cos^2(α))^2

Now, the expression becomes:

sin^2(α) + (cos^2(α))^2

And using the identity again, we get:

sin^2(α) + sin^2(α) = 2 * sin^2(α)

So, the simplified expression is:

2 * sin^2(α)