21.
a) `2sin(x-30^@)-1=0`
`<=>sin(x-30^@)=1/2`
`<=> sin(x-30^@)=sin30^@`
`<=>[(x-30^@=30^@+k360^@),(x-30^@=180^@-30^@+k360^@):}`
`<=> [(x=60^@+k360^@),(x=180^@+k360^@):}`
b) `5sin^2x+3cosx+3=0`
`<=>5(1-cos^2x)+3cosx+3=0`
`<=>-5cos^2x+3cosx+8=0`
`<=>(cosx+1)(cosx=8/5)=0`
`<=>[(cosx=-1),(cosx=8/5\ (VN)):}`
`<=>x=180^@+k360^@`
22.
`-1<=sin2x<=1`
`<=>2<=3+sin2x<=4`
`=> y_(min)=2 ; y_(max)=4`

1. B
2. A
3. A
4. C
5. B
6. A
7. A

18. The cook told me to mix the eggs with the flour.

19. Luke told me to bring a bottle of wine to the party.

20. Mon said to me that I should not eat out too often.

`\sqrt((-1)/(2x)) .\sqrt(-8x^5)`

`=\sqrt( (-1)/(2x) . (-8x^5))`

`=\sqrt( 8x^5)/(2x))`

`=\sqrt(4x^2)`

`=|2x|=-2x`

`sin^2 α+cos^2 α =1`

`=> sinα =\sqrt(1-cos^2α)=\sqrt(1-(3/4)^2) = \sqrt7/4`

`=> tanα=(sinα)/(cosα)=(3\sqrt7)/7`

`=> cotα=1/(tanα)=\sqrt7/3`

`(3-\sqrt5)(\sqrt10+\sqrt2)(3-\sqrt5)`

`=(3-\sqrt5)^2 .(\sqrt10+\sqrt2)`

`=(3-6\sqrt5+5)(\sqrt10+\sqrt2)`

`=(8-6\sqrt5)(\sqrt10+\sqrt2)`

`=2\sqrt10 -22\sqrt2`

`=(3x-1)^2+2(2x-1)(2x+5)+(2x+5)^2-(2x-3)(4x^2+6x+9):(2x-3)`

`=(3x-1)^2+2(2x-1)(2x+5)+(2x+5)^2-(2x-3)(4x^2+6x+9):(2x-3)`

`=(3x-1+2x+5)^2-(4x^2+6x+9)`

`=(5x+4)^2-(4x^2+6x+9)`

`=25x^2+40x+16-4x^2-6x-9`

`=21x^2+34x+7`

`2(x-4)-3(x+1)=4`

`2x-8-3x-3=4`

`2x-3x=4+8+3`

`-x=15`

`x=-15`

`3(x+5)-3=2(x+1)+7`

`3x+15-3=2x+2+7`

`x=-3`

.

`15-(x+2)^2=-1`

`(x+2)^2=16`

`(x+2)^2=4^2=(-4)^2`

`[(x+2=4),(x+2=-4):}`

`[(x=2),(x=-6):}`

.

`75-(2x+1)^3=11`

`(2x+1)^3=64`

`(2x+1)^2=4^3`

`2x+1=4`

`x=3/2`

Áp dụng hệ thức trong tam giác vuông:

`MH^2 =NH.PH`

`=>PH=MH^2 : NH = 2,4^2 : 1,8=3,2(cm)`

`=> NP=NH+PH=5(cm)`

`=> S= 1/2 . MH .NP =6(cm^2)`