Question

Распишите полное решение данных тригонометрических выражений.

Answer 1

1) sin(a-b)+cos a*sin b =sina*cosb - cosa*sin b+cos a*sin b=sin a*cos b

2) cos(пи/2 - t)*ctg(-t)/sin (пи/2+t) = - sin t *ctg t/cos t =(-sint*cost/sint)/cost =

= -cost/cost = -1 

3) ctg(-t)*sin t +cos(пи + t)=-cost/sint*sin t -cost =-cost-cost=-2cost

Answer 2

$1)\ sin(\alpha-\beta)+cos\alpha sin\beta=sin\alpha cos\beta-sin\beta cos\alpha+cos\alpha sin\beta =sin\alpha cos\beta;$

$2)\ \frac{cos(\frac{\pi}{2}-t)*ctg(-t)}{sin(\frac{\pi}{2}+t)}=\frac{sint*ctg(-t)}{cost}=tgt*-(ctgt)=-1;$

$3)\ ctg(-t)*sint+cos(\pi+t)=-\frac{cost}{sint}*sint-cost =-cost-cost=-2cost.$