Question

Hitungalah nilai dari trigonometri berikt!
A. Cos 75° cos 15°
B. -2 sin 15° sin 75°

Answer 1

Cos 75°=cos (45°+30°)
= cos 45° cos 30° - sin 45° sin 30°
= ½√2.½√3 - ½√2.½
= ¼√6 - ¼√2
= ¼(√6-√2)
cos 15°= cos (45°-30°)
= cos 45° cos 30° + sin 45° sin 30°
= ¼(√6+√2)

cos 75° cos 15°=¼(√6+√2).¼(√6-√2)
= (¼√6)²-(¼√2)²
=6/16 - 2/16
= ¼

sin 75°= sin (90°-15°)
= cos 15°
= ¼(√6+√2)
sin 15°= sin (90°-15°)
= cos 75°
= ¼(√6-√2)

-2 sin 15° sin 75°= -2 cos 75° cos 15°
= -2 (¼)
= -½

Answer 2

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