tgα=sinα/cosα
ctgα=cosα/sinα        
tgα*ctgα=1
sin²α+cos²α=1       
1+ tg²α=1/cos²α         
1 + ctg²α=1/sin²α

Լրացուցիչ առաջադրանքներ

Վարժ. 115

ա)|3x-5|=7

3x-5=7
3x-5=-7

x=4
x=-2/3

բ)|6x-7|-7x=1

6x-7-7x=1 , 6x-≥0
-(6x-7)-7x=1,  6x-7<0

x=-8 , x≥7/6
x=6/13 , x<7/6

x ⋲ Ø
x=6/13

x=6/13

գ)|8x-4|=|9x-5|

8x-4=9x-5
8x-4=-(9x-5)

x=1
x=9/17

Վարժ. 116

ա) |2-7x|<5

2-7x<5 , 2-7x≥0
-(2-7x)<5 , 2-7x<0

x>-3/7 , x≤2/7
x<1, x>2/7

x ⋲ (-3/7, 2/7]
x ⋲ (2/7, 1]

x ⋲ (-3/7, 1)

բ) |5x-5|≥2

5x-5≥2 , 5x-5≥0
-(5x-5)≥2 , 5x-5<0

x≥7/5 , x≥1
x≤3/5 , x<1

x ⋲ [7/5 , +~)
x ⋲ (-~ , 3/5]

x ⋲ [-~ , 0,6) U [1,4, +~)

գ) |7x+2| ≤ |3-x|

|7x+2|-|3-x| ≤ 0

7x+2-(3-x) ≤ 0 , 7x+2 ≥ 0 , 3-x ≥ 0
-(7x+2)-(3-x) ≤ 0 , 7x+2<0 , 3-x ≥ 0
7x+2-(-(3-x)) ≤ 0 , 7x+2 ≥ 0 , 3-x<0
-(7x+2)-(-(3-x)) ≤ 0 , 7x+2<0 , 3-x<0

x ≤ 1/8 , x ≥ -2/7 , x ≤ 3
x ≥ -5/6 , x<-2/7 , x ≤ 3
x ≤ -5/6 , x ≥ -2/7, x>3
x ≥ 1/8 , x<-2/7 , x>3

x ≤ 1/8 , x ⋲ [-2/7 , 3]
x ≥ -5/6 , x ⋲ (-~ , -2/7)
x ≤ -5/6 , x ⋲ (3, +~)
x ≥ 1/8 , x ⋲ Ø

x ⋲ [-2/7 , 1/8]
x ⋲ [-5/6, -2/7)
x ⋲ Ø
x ⋲ Ø

x ⋲ [-5/6 , 1/8]