Question

решить тригонометрические уравнения:
а) tg x/10=1
б) tg12x=1
в) tg(3x-π/2)=1
г) tg(x-2)= -1
д) tg10x=0

Answer 1

1. tg(x/10)=1; x$\neq$5$\pi$+10$\pi$n

x/10 = $\pi$/4 + $\pi$n

x = 5$\pi$/2+10$\pi$n

2. tg(12x)=1; x$\neq$$\pi$/24 + $\pi$n/12

12x = $\pi$/4 + $\pi$n

x = $\pi$/48 + $\pi$n/12

3. tg(3x-$\pi$/2)=1; x$\neq$$\pi$n/3

3x-$\pi$/2 = $\pi$/4 +$\pi$n

3x = 3$\pi$/4 +$\pi$n

x = $\pi$/4 + $\pi$n/3

4. tg(x-2)=-1; x$\neq$$\pi$/2+2+$\pi$n

x-2 = - $\pi$/4 + $\pi$n

x = -$\pi$/4 + 2 + $\pi$n

5. tg(10x)=0; x$\neq$$\pi$/20+$\pi$n/10

10x = $\pi$n

x = $\pi$n/10