Question

Докажите тождества
помогите пожалуйста​

Answer 1

Ответ:

Объяснение:

$a) \frac{cos(\alpha -\beta )}{sin\alpha *cos\beta } =ctg\alpha +tg \beta \\\frac{cos\alpha*cos\beta +sin\alpha *sin\beta }{sin\alpha *cos\beta } = \frac{cos\alpha *cos\beta }{sin\alpha *cos\beta } +\frac{sin\alpha *sin\beta }{sin\alpha *cos\beta } =\frac{cos\alpha }{sin\alpha } +\frac{sin\beta }{cos\beta } =ctg\alpha +tg\beta$

b) sin (π/6+α)+sin(π/6-α)= sin(π/6)*cosα+cos(π/6)*sin α+sin(π/6)*cosα-cos(π/6)*sin α =2sin(π/6)*cosα=2*0.5*cosα=cosα

$c) \frac{sin(\alpha -\beta )}{cos\alpha *cos\beta }= \frac{sin\alpha *cos\beta -cos\alpha *sin\beta }{cos\alpha *cos\beta} = \frac{sin\alpha *cos\beta }{cos\alpha *cos\beta} -\frac{cos\alpha *sin\beta }{cos\alpha *cos\beta} = \frac{sin\alpha }{cos\alpha }-\frac{sin\beta }{cos\beta } =\\\\=tg\alpha -tg\beta$

d) cos (π/6+α)- cos(π/6-α)= cos (π/6)*cos(α)-sin(π/6)*sin(α) - cos (π/6)*cos(α)+sin(π/6)*sin(α) =2*sin (π/6)*sin(α)=2*0.5*sinα=sinα