Cos2x+8sinx-7=0
cos^2x-sin^2x+8sinx-7=0
1-sin^2x-sin^2x+8sinx-7=0
-2sin^2x+8sinx-6=0
sin^2x-4sinx+3=0
Заменим sinx на a:
a^2-4a+3=0 а€[-1;1]
По теореме Виета решим квадратное уравнение:
а1=1;а2=3-не удовлетворяет условию
При sinx=1: х=arcsin(1)=90
1/(1+√2) = (√2–1)/((√2–1)(√2+1)) = (√2–1)/(2–1) = √2–1,
1/(√2+√3) = (√3–√2)/((√3–√2)(√3+√2)) = (√3;–√2)/(3–2) = √3–√2,
. .
1/(√2004+√2005) = (√2005–√2004)/((√2005–√2004)(√2005+√2004)) = (√2005–√2004)/(2005–2004) = √2005–√2004.
<span>Сумма равна √2–1+√3–√2+…+√2005–√2004 = √2005–1.</span>
5x(3x+7)+(4x+1)^2=-19x+63; 15x^2+35x+16x^2+8x+1+19x-63=0; 31x^2+62x-62=0;
x^2+2x-2=0
Енто по формулам двойного синуса <span>
(sin16*cos16*cos32*cos64) / sin52 = sin32/2*cos32cos64/sin52=sin64/4*cos64/sin52 = sin128/8sin52=sin(180-52)/8sin52 =
=sin52/8sin52=1/8
валшебник !!!!</span>
(х+2+7)(х+2-7)=0
(х+9)(х-5)=0
ответ: х1=-9; х2=5