Question

Упростите выражение tg a/tg 2a-tg a

Answer 1

Решение на фотографии

Answer 2

Simplifying the Expression tg(a)/tg(2a)-tg(a)

To simplify the expression tg(a)/tg(2a)-tg(a), we can use trigonometric identities and properties. First, let's express tg(2a) in terms of tg(a).

Using the identity tg(2a) = 2tg(a)/(1-tg^2(a)), we can substitute tg(2a) in the expression.

So, tg(a)/tg(2a)-tg(a) becomes tg(a)/(2tg(a)/(1-tg^2(a)))-tg(a).

Now, let's simplify this expression step by step.

1. tg(a)/(2tg(a)/(1-tg^2(a)))-tg(a) 2. tg(a) * (1-tg^2(a))/(2tg(a)) - tg(a) 3. (tg(a) - tg(a) * tg^2(a))/(2tg(a)) - tg(a) 4. (tg(a) - tg^3(a))/(2tg(a)) - tg(a) 5. tg(a) - tg^3(a)/(2tg(a)) - tg(a) 6. tg(a) - tg^2(a)/2 - tg(a)

So, the simplified expression is tg(a) - tg^2(a)/2 - tg(a).

This is the simplified form of the given expression.