1) sin <u>2π</u> + sin<u> π </u>= 2 sin <u>2π+π</u> cos<u> 2π-π</u> = 2 sin <u>3π</u> cos <u>π </u>
5 5 5*2 5*2 10 10
2) cos<u> 11π </u>+ cos <u>3π </u>= cos<u>11π</u> + cos <u>9π </u>= 2 cos <u>11π+9π</u> cos <u>11π-9π </u>=
12 4 12 12 12*2 12*2
=2 cos <u>20π</u> cos<u> 2π </u>= 2 cos<u> 5π </u>cos <u>π </u>
24 24 6 12
3) cos(π/3 - α) + cosα =2 cos<u>(π/3 - α+α)</u> cos (<u>π/3 -α-α</u>) =
2 2
=2 cos <u>π </u>cos(<u>π </u>- α) = 2 *<u>√3 </u>cos(<u>π </u>- α) = √3 cos(<u>π </u>- α)
6 6 2 6 6
=√3 (cos<u>π </u>cosα + sin<u>π </u>sinα) =√3 (<u>√3</u> cosα + <u>sinα</u>)
6 6 2 2
4) sin(π/6 +α) - sin(π/6 -α) = 2 sin<u> (π/6 +α-π/6+α)</u> cos<u>(π/6 +α+π/6-α)</u> =
2 2
=2 sinα cosπ/6 = 2 * <u>√3 </u>sinα =√3 sinα
2
5) sin π/6 - sin π/9 = sin 3π/18 - sin 2π/18 =
= 2 sin<u> (3π-2π)</u> cos <u>(3π+2π) </u>= 2 sin <u>π </u> cos <u>5π</u>
18*2 18*2 36 36
6) sinα - sin (α +π/3) = 2 sin<u> (α-α-π/</u>3) cos <u>(α+α+π/3)</u> =
2 2
=2 sin (-π/6) cos(α+π/6) = -2 * (1/2) cos(α + π/6) =
=-cos(α+π/6) = -(cosα cosπ/6 - sinα sin π/6) =
= -(<u>√3</u> cosα - (1/2) sinα) =<u>1 </u>(sinα - √3 cosα)
2 2
25y²-1=0
25y²=1
y²=1/25
y=±1/5
-y²+2=0
-y²=-2
y²=2
y=±√2
9-16y²_0
y²=9/16
y=±3/4
7y²+y=0
y(7y+1)=0
y1=0; y2=-1/7
4y-y²=-y(y-4)=0
y1=0
y2=4
0.2y²-y=0
y(0.2y-1)=0
y1=0
y2=5
(x+2)(x-1)=0
x1=-2
x2=1
У=6sinx+8cos2x
у є [-14;14]
Решение смотри в приложении