jika 1/2phi < x
Matematika
andika634
Pertanyaan
jika 1/2phi < x <phi dan tan x = -a , maka ( sin x + cos x )2 sama dengan =
2 Jawaban
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1. Jawaban MIPAStudyCenterID
[tex]\text{Batasnya : }90^o \ \textless \ x \ \textless \ 180^o\\\\\text{Tan x = -a}\\\text{Depan = a, Samping = -1, Miring = } \sqrt{a^2 + 1}\\\\\text{Maka...}\\\text{(Sin x + Cos x)}^2\\= ( \frac{a}{ \sqrt{a^2 + 1} } - \frac{1}{ \sqrt{a^2 + 1} })^2\\= ( \frac{a - 1}{ \sqrt{a^2 + 1} })^2\\= \frac{a^2 - 2a + 1}{a^2 + 1} [/tex]
║MIPA Study Center ID║ -
2. Jawaban DB45
Trigonometri
tan x = - a dan x di kuadran II
tan x = y/x
y = a, x = 1 , r = √(x²+y²) = √(a²+1)
sin x = y/r = a/√(a²+1)
cos x = - x/r = -1/√(a²+1)
(sin x + cos x)² = (a/ √(a²+1) - 1/√(a²+1)}²
(sin x + cos x)² = {(a-1)/√(a²+1)²}
(sin x + cos x)² = (a -1)²/(a²+1)