<span>(Cosx+sinx)^2=cos2x</span>
<span>cos^2x +2sinxcosx+sin^2x=cos2x</span>
<span>sin2x+1-cos2x=0</span>
<span>2sinxcosx+sin^2x+cos^2x-cos^2x+sin^2x=0</span>
<span>2sinx(sinx+cosx)=0</span>
<span>sinx=0</span>
<span>x=ПN</span>
<span>sinx=-cosx/ /cosx</span>
<span>tgx=-1</span>
<span>x=-п/4+пN</span>
1) (4a-b)(a-6b)+a(25b-3a)=4a²-24ab-ab+6b²+25ab-3a²=
4a²-<u>25ab</u>+<u>25ab</u>+6b²-3a²=<u>4a²</u>-<u>3a²</u>+6b²=<u>a²+6b²
</u>
2) (2x+3y)(x-y)-x(x+y)=2x²<u>-2xy</u>+<u>3xy</u>-3y²-x²<u>-xy=</u>2x²-x²-3y²=x²-3y²
3) 3a(a+1)+(a+2)(a-3)=<u>3a²</u>+3a+<u>a²</u>-3a+2a-6=<u>4a²+2a-6
</u>4) 2c(5c-3)-(c-2)(c-4)=<u>10c²-</u>6c-<u>c</u>²+4c+2c-8=9c²<u>-6c</u>+<u>4c</u>+<u>2c</u>-8=<u>9c²-8</u>
1+cosa-2sina/2cosa/2=2cos^2a/2-2sina/2cosa/2=2cosa/2(cosa/2-sina/2)=
=2cosa/2(cosa/2-cos(п/2-a/2))=4cosa/2sinП/4sin(П/4-a/2)=2√2cosa/2sin(П/4-a/2)
sin3a(cosa-cos3a)=sin3acosa-1/2sin6a=1/2sin4a+1/2sin2a-1/2sin6a=1/2(sin2a+sin4a-sin6a)
(1/2)^(10-3x)=32
2^-(10-3x)=2^5
3x-10=5
3x=15
x=5
Sin(a-b-2a)=sin(-a-b)=-sin(a+b)