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6cos52,5°sin7,5°

6cos52,5°sin7,5°

jawaban untuk soal di atas adalah (3/2)(√3 – √2)

Asumsi soal:
Tentukan nilai dari 6 cos 52,5⁰ sin 7,5⁰

Ingat kembali:
2 cos A sin B = sin (A+B) – sin (A–B)
sin 45⁰ = ½√2
sin 60⁰ = ½√3

Ingat juga:
ab –ac = a(b –c)
a × (1/b) = a/b

6 cos 52,5⁰ sin 7,5⁰
= 3 × (2 cos 52,5⁰ sin 7,5⁰)
= 3 × {sin (52,5⁰+7,5⁰) – sin (52,5⁰–7,5⁰)
= 3 × (sin 60⁰ – sin 45⁰)
= 3 × (½√3 – ½√2)
= 3 × ½(√3 – √2)
= (3/2)(√3 – √2)

Jadi, nilai dari 6 cos 52,5⁰ sin 7,5⁰ adalah (3/2)(√3 – √2)

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