cos⁴(5/12π)-sin⁴(5/12π) =.... bantu q beri poin bsr...

Trigonometri.
Kelompok peminatan kelas XI kurikulum 2013 revisi 2016.

a⁴ - b⁴ = (a² + b²)(a² - b²)
cos² x = 1/2 (1 + cos 2x)
sin² x = 1/2 (1 - sin 2x)

cos⁴ (5/12 π) - sin⁴ (5/12 π) = cos⁴ 75° - sin⁴ 75°
= (cos² 75° + sin² 75°) (cos² 75° - sin² 75°)
= [1/2 (1 + cos 150°) + 1/2 (1 - cos 150°)] [1/2 (1 + cos 150°) - 1/2 (1 - cos 150°)]
= [1/2 (2)] [1/2 (2 cos 150°)]
= 1 (-1/2 √3)
= -1/2 √3

jawaban terlampir mohon dipahami ya