Question

Cos(2a) + 1 / ctg(a)

Answer 1

Не уверена........................

Answer 2

To simplify the expression, let's work on each term separately:

1. Cos(2a):

Using the double angle formula for cosine, we have:

cos(2a) = cos^2(a) - sin^2(a)

2. 1 / ctg(a):

Recall that cotangent (ctg) is the reciprocal of the tangent function:

ctg(a) = 1 / tan(a)

Now, let's substitute the expressions we obtained into the original expression:

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

Next, simplify the expression further:

= cos^2(a) - sin^2(a) + tan(a)

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

= (1 - sin^2(a)) - sin^2(a) + tan(a)

= 1 - 2sin^2(a) + tan(a)

This is the simplified form of the expression cos(2a) + 1 / ctg(a).