Question

Синус 3 альфа разделить, на синус альфа, плюс, косинус 3 альфа, разделить на косинус альфа. (ДВЕ ДРОБИ) УПРОСТИТЬ ВЫРАЖЕНИЕ

Answer 1

Sin 3a / Sin a  +  Cos 3a / Cos a = 
= (3Sin a - 4Sin³ a) / Sin a + ( 4Cos³ a -3 Cos a) / Cos a=
=3 - 4Sin² a + 4Cos² a - 3 =  4Cos² a - 4Sin² a = 4( Cos² a - Sin² a) = 4 Cos 2a

Answer 2

Simplifying the Expression

To simplify the expression sin(3α) / sin(α) + cos(3α) / cos(α), we can use trigonometric identities to rewrite the terms in a more manageable form.

Let's start by expressing sin(3α) and cos(3α) in terms of sin(α) and cos(α) using the triple angle formulas:

sin(3α) = 3sin(α) - 4sin^3(α). **cos(3α) = 4cos^3(α) - 3cos(