Question

MATEMATIKA PEMINATAN IPA SMA

Jika 1 - cot α = -1/3 maka nilai sin2α + cos2α =.....

A. 17/25
B. 1
C. 6/5
D. 31/25
E. 7/5


Tolong jawaban lengkap dan pakai cara.

Answer 1

1 - cota = -1/3
-cota = -1/3 - 3/3
-cota = -4/3
cota = 4/3

cosa/sina = 4/3

samping = 4, depan = 3
miring = √4² + 3²
= √16 + 9
= √25
= 5

sina = 3/5
cosa = 4/5
tana = 3/4

sin2a + cos2a = sin(a + a) + cos(a + a)
= (sina cosa + sina cosa) + (cosa cosa - sina sina)
= ((3/5)(4/5) + (3/5)(4/5)) + ((4/5)(4/5) - (3/5)(3/5))
= (12/25 + 12/25) + (16/25 - 9/25)
= (24/25) + (7/25)
= 31/25
→ D.