Question

Jika π/2 < x < π dan tan x = a maka (sin x + cos x) kuadrat sama dengan

Answer 1

X di kuadran II
tan x    = - a
sin a =  a/ √(a²+1)
cos a = - 1/√(a²+1)

(sin a + cos a)² = 1 + 2 sin a cos a
(sin a + cos a)² = 1 + 2( -a/(a²+1) = 1  - 2a/(a²+1) = (a²+1 - 2a)/(a²+1)
(sin a + cos a)² = (a-1)²/(a²+1)