Question

Найдите значение выражения

$frac{sin alpha +cos alpha }{sin alpha -cos alpha }$ , если tg$alpha$=$frac{5}{4}$

Answer 1

tga=5/4
cos²a=1:(1+tg²a)=1:(1+25/16)=16/41
cosa=4/√41
sina=√(1-cos²a)=√(1-16/41)=√25/41=5/√41
(sina+cosa)/(sina-cosa)=(5/√41+4/√41):(5/√41-4/√41)=9/√41*√41/1=9

Answer 2

(sina+cosa)/(sina- cosa) =(tqa+1)/(tqa-1) =(5/4+1)/(5/4-1) =9.