Question

(1 + ctg²а) * sin²α =

Answer 1

Упростить:

(1+ctg^2a)×sin^2a = (1/sin²a) * sin²a = 1

Решение:

(Нужно его упростить, как показано выше).

Answer 2

The expression you provided is:

(1 + ctg²α) * sin²α

To simplify this expression, let's rewrite ctg²α as cot²α, since ctg is often used to represent cotangent.

Using trigonometric identities, we know that cot²α + 1 = csc²α, where csc is the cosecant function. Rearranging this equation, we have cot²α = csc²α - 1.

Substituting this into the original expression, we get:

(1 + (csc²α - 1)) * sin²α

Simplifying further:

(1 + csc²α - 1) * sin²α

The 1 and -1 terms cancel out:

csc²α * sin²α

Since csc²α is equal to (1/sin²α), we can substitute it:

(1/sin²α) * sin²α

The sin²α terms cancel out, leaving us with:

1

So, the simplified expression is 1.