Տնային աշխատանք հանրահաշվից

1. Լուծել հավասարումը

ա) 2sin²x – sinx = 0

sinx * (2sinx – 1) = 0

x = 0

2sinx – 1 = 0

sinx = 0

sinx = 1/2

x = +- pk, k- z

x = p/6 + 2pk, k- z

գ) tg²x – tgx = 0

tgx * (tgx – 1) = 0

(tgx – 1 = 0)

p/4 + pk, k- z = +- pk, k- z

դ) 5cosx = sin2x

5cosx – 2sinx cosx = 5

cosx * (5 – 2sinx²)

cosx = 0

sinx < 5/2 = 5

x = 4/2 = 2pk

x = p/k + 2pk

5 = 3p/6 + 10k

2. Լուծել հավասարումը

ա) 2sinx + tg * (p – x) = 0

բ) ctg x/2 + cos * (p – x) = 1

sinx/1 + cosx – cosx = 1

sinx – (1 + cosx) * cosx/1 + cosx = 1

sinx – cosx – cos²x = 1 + cosx

sinx – 2cosx – cos²x – 1 = 0

sinx – 2cosx – cos²x – sin²x – cos²x = 0

sinx – 2cosx – 2cos²x – sin²x = 0

sinx * (1 – sinx) – 2cosx * (1 + cosx) = 0, sinx * cosx

1 – sinx/cosx * 2 * (1 + cosx)/sinx = 0

tg x/2 – 2 * 1/ctgx/2 = 0

tg x/2 – 2 * tg x/2 = 0

tg x/2 = 0

x/2 = +- pk

x = +- 2pk, k- z