f(x)=-4cosx+2/sin^2x

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вопрос

Given function is f(x) = -4cos(x) + 2/sin^2(x)

To simplify the expression, we have to rewrite the terms using trigonometric identities.

Using the identity: sin^2(x) + cos^2(x) = 1

We can rewrite the function f(x) as:
f(x) = -4cos(x) + 2/(1 - cos^2(x))

Now to simplify further, we need to express cos^2(x) in terms of sin(x).

Using the same trigonometric identity: sin^2(x) = 1 - cos^2(x)

We get: cos^2(x) = 1 - sin^2(x)

Substitute this expression back into the function f(x):
f(x) = -4cos(x) + 2/sin^2(x)

f(x) = -4cos(x) + 2/(1 - sin^2(x))

f(x) = -4cos(x) + 2/cos^2(x)

Therefore, the simplified expression of f(x) is:
f(x) = -4cos(x) + 2/cos^2(x)