Question

найти tg a, если sin2a=0,8 и п<а<3п/2​

Answer 1

sin 2a = 4/5

π < a < 3π/2

tg a - ?, tg a = t

2t/1+t² = 4/5 (универсальная триганометрическая подстановка)

2t/1+t² - 4/5 = 0

10t-4-4t² = 0

2t²-5t+2 = 0

t²-2.5t+1 = 0

По Теореме Виета:

{t1+t2 = 2.5

{t1•t2 = 1

t1 = 2

t2 = 0.5

1)tg a = 2

tg a = 1/2