Cos a- sin a/sin a* cos a +sin a/ 2cos a

(sin(3п/2+a)+sin(2п+a)/(2cos(-a)sin(-a)+1)=

=-cos a + sin a / (2 cos a * (-sin a) +1) =

=-cos a + sin a / (-2 cos a * sin a + (cos a)^2 +2 cos a * sin a + (sin a)^2 )=

= -cos a + sin a /    ((cos a)^2  + (sin a)^2) =

= -cos a + sin a / 1 = sin a - cos a

источник:

Решение 1.7^2x-6*7^x+5=07^x = tt²- 6t + 5 = 0 t₁   = 1t₂   = 51)   7^x = 17^x = 7^0x₁   = 02)   7^x = 5xlg7 = lg5x₂   = lg5  /  lg72.4^x+2^x=12  2^2x  +  2^x  -  12 = 0 2^x = t , t  > 0t² +    t - 12 = 0t₁ = - 4 не удовлетворяет условию    t  > 0 t₂ = 3 2^x = 3xlg2 = lg3x = lg3 / lg23.13^x+1=169^x13^2x -  13^x -  1 = 0t = 13^x, t > 0 t² - t - 1 = 0 d = 1 + 4*1*1 = 5 t₁ = (1 -   √5)/2 < 0 не удовлетворяет условию t > 0 t₂ = (1 +  √5)/2 13^x =  (1 +  √5)/2xlg13 = lg[ (1 +   √5)/2]x =    lg[ (1 +   √5)/2] / lg13

в). 3x² + 5x - 2 = 3(x - 1/3)(x + 2) = (3x - 1)(x+ 2);

    3x² + 5x - 2 = 0         d = b²-4ac = 25+24 = 49

    x₁ = (-b+√d)/2a = (-5+7)/6 = 1/3

    x₂ = (-b-√d)/2a = (-5-7)/6 = -2        

г). 6x² - 13x + 6 = 6(x - 1,5)(x - 2/3) = (2x - 3)(3x - 2);

    6x² - 13x + 6 = 0         d = b²-4ac = 169-144 = 25

    x₁ = (-b+√d)/2a = (13+5)/12 = 1,5

    x₂ = (-b-√d)/2a = (13-5)/12 = 2/3