Question

(cosx)^4 + (sinx)^4 = |sinx * cosx|

Answer 1

Ответ:

Объяснение:

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Answer 2

Let's simplify the equation step by step.

Starting with the left-hand side (LHS) of the equation:

(cosx)^4 + (sinx)^4

We can rewrite this using the identity (cosx)^2 + (sinx)^2 = 1:

[(cosx)^2]^2 + [(sinx)^2]^2

Since (cosx)^2 + (sinx)^2 = 1, we can substitute it in:

(1 - (sinx)^2)^2 + (sinx)^4

Expanding the equation:

(1 - 2(sin^2x) + (sin^4x)) + (sin^4x)

Combining like terms:

1 - 2(sin^2x) + 2(sin^4x)

Now, let's simplify the right-hand side (RHS) of the equation:

|sinx * cosx|

Since the absolute value of a product is equal to the absolute value of each factor, we can rewrite it as:

|sinx| * |cosx|

Since |cosx| is always positive, we can further simplify it to:

|sinx * cosx|

So the right-hand side of the equation is the same as the right-hand side in the original equation.

Now we have:

1 - 2(sin^2x) + 2(sin^4x) = |sinx * cosx|

It appears that the original equation is not true for all values of x. Some values may satisfy the equation, but it's not a universally valid identity.