3tg(x/2) + ctgx=5/sinx

Tg (x/2) + ctg x = sin (x/2)/ cos (x/2) + cos x / sin x =
 = (sin (x/2)·sin x + cos x·cos (x/2)) / (cos (x/2)·<span>sin x </span>) =
= cos (x - x/2) / (cos (x/2)·sin x <span>) =
= </span>cos (x/2) / (cos (x/2)·sin x )  = 1 / <span>sin x 

2tg (x/2) + </span>1 / <span>sin x  = 5 / sin x
</span>2tg (x/2) = 5 / sin x - 1 / <span>sin x 
</span>2tg (x/2) <span>= 4/ sin x
</span>tg (x/2) <span>= 2/ sin x
</span>
tg (x/2) =√((1 - cos x) / (1 + cos x)) = (1 - cos x)/ sin x

(1 - cos x)/ sin x = 2<span>/ sin x
</span>(1 - cos x - 2<span>)/ sin x = 0
</span>(cos x + 1<span>)/ sin x = 0</span>
cos x = -1 при этом sin x≠0
Получается, нет корней