2) sin a = 5/13; pi/2 < a < pi Если pi/2 < a < pi, то sin a > 0; cos a < 0 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) в) г) 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
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1) Табличные значения5sin 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
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)
в)
г)
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