tg (x+20°)+tg(70°-x) =2 .очень прошу помочь...

kabirova1 @kabirova1

July 2022 1 10 Report

tg (x+20°)+tg(70°-x) =2
.очень прошу помочь

Answers & Comments

kovalenina $tg(x+20)+tg(70-x)=2$
$tg(x+20) + tg(90-20-x) = 2$
$tg(x+20) + ctg(x+20) = 2$
$\frac{sin(x+20)}{cos(x+20)}+ \frac{cos(x+20)}{sin(x+20)} = \frac{ sin^{2}(x+20)+cos^{2}(x+20) }{cos(x+20)sin(x+20)} =2$
$\frac{1}{cos(x+20)sin(x+20)}=2$
2cos(x+20)sin(x+20) = 1
sin(2x+40) = 1
2x + 40 = $\frac{ \pi }{2}+2 \pi n$
2x = 45 -40 + $2 \pi n$
x = 2,5 + $\pi n$ , n∈Z

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