Question

Cos^2 a + tg(-a)ctg a

Answer 1

Ответ:

Объяснение:

cos^2 - tga * ctg a = cos^2 - 1 = - sin^2a

Answer 2

cos^2 a + tg (-a) • ctg a = cos^2 a - (sin a/cos a) • (cos a/sin a) = cos^2 a - 1 = - sin^2 a

Ответ: - sin^2 a.

Answer 3

Let's work through the expression step by step:

1. cos^2(a) represents the square of the cosine of angle a.
2. tg(-a) represents the tangent of the negative of angle a. Since the tangent function is an odd function (i.e., tan(-x) = -tan(x)), you can simplify tg(-a) as -tan(a).
3. ctg(a) represents the cotangent of angle a, which is the reciprocal of the tangent, so ctg(a) = 1/tan(a).

Now, let's substitute these values into the expression:

cos^2(a) + tg(-a)ctg(a) = cos^2(a) + (-tan(a))(1/tan(a))

The term (-tan(a))(1/tan(a)) simplifies to -1 because the tangents cancel out:

cos^2(a) + (-1)

So the final result is:

cos^2(a) - 1