Ask and Answer for Adinda (trigonometri)

Ask #01 24 Maret 2017
Assalamu alaikum Ask and Answer, saya mau bertanya soal bab trigonometri

Jika sin(2x + 75) = a dan sin(x + 45) = b,
maka cos(3x + 120)cos(x + 30) =

Answer #01 24 Maret 2017
Waalaikum salam Adinda, Baik kakak jawab

Ingat rumus :

2cos a cos b = cos (a + b) + cos (a - b)

= cos(3x + 120)cos(x + 30)
= 0.5{cos{(3x + 120) + (x + 30)} + cos{(3x + 120) - (x + 30)}}
= 0,5{cos(4x + 150) + cos(2x + 90)}
= 0,5{cos2(2x + 75) + cos2(x + 45)}

Ingat rumus sudut rangkap
cos 2x = 1 - 2 sin ^2 x

= 0,5{1 - 2 sin ^ 2 (x + 75) + 1 - 2 sin ^ 2 (x + 45)}
= 0,5{1 - 2 a^2 + 1 - 2 b^2}
= 0,5{2 - 2 a^2 - 2 b^2}
= 1 - a^2 - b^2

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