Помогите м алгеброй. Вообще эту тему не понимаю.

1) Табличные значения
5sin 0 + 3cos 60 = 5*0 + 3*1/2 = 3/2
2sin pi/2 - 3tg pi/4 = 2*1 - 3*1 = -1
4tg (-pi/4) - cos 300 = 4(-1) - cos(-60) = -4 - 1/2 = -4,5

2) sin a = 5/13; pi/2 < a < pi
Если pi/2 < a < pi, то sin a > 0; cos a < 0<br>Основное тождество: sin^2 a + cos^2 a = 1
cos a = -√(1 - sin^2 a) = -√(1 - 25/169) = -√(144/169) = -12/13
tg a = sin a / cos a = (5/13) / (-12/13) = -5/12
ctg a = 1 / tg a = -12/5

3) а) 1 - sin a*cos a*tg a = 1 - sin a*cos a*sin a / cos a =
= 1 - sin^2 a = cos^2 a
б) $\frac{cos a}{1+sin a} + \frac{1+sin a}{cos a} = \frac{cos^2 a + (1 + sin a)^2}{cos a(1+sin a)} = \frac{cos^2 a+1+2sina+sin^2a}{cos a(1+sin a)} =$
$= \frac{2+2sina}{cos a(1+sin a)} = \frac{2}{cosa}$
в) $cos a + sin a*tg a = cos a + sin a* \frac{sin a}{cos a} = \frac{cos^2 a + sin^2 a}{cos a}= \frac{1}{cos a}$
г) $\frac{1-sin^2a}{cos^2a-1}-1 = \frac{1-sin^2a-cos^2a+1}{cos^2a-1}= \frac{1}{-sin^2a} =-\frac{1}{sin^2a}$
д) (sin a + cos a)^2 + (sin a - cos a)^2 = sin^2 a + 2sin a*cos a + cos^2 a + sin^2 a - 2sin a*cos a + cos^2 a = 2
е) cos^4 a - sin^4 a + sin^2 a = (cos^2 a - sin^2 a)(cos^2 a + sin^2 a) + sin^2 a = cos^2 a - sin^2 a + sin^2 a = cos^2 a