Jawaban:

sin^2 x = 1/2 - 1/2.cos 2x

cos^2 x = 1/2 + 1/2.cos 2x

sin^2 x + cos^2 x = 1

x = 15

sin^6 x - cos^6 x

= (sin^2 x)^3 - (cos^2 x)^3

= (1/2 - 1/2.cos 2x)^3 - (1/2 + 1/2.cos 2x)^3

Let

a = 1/2.cos 2x

(1/2 - a)^3 - (1/2 + a)^3

= (1/2 - a) (1/2 - a)(1/2 - a) - (1/2 + a)(1/2 + a)(1/2 + a)

= (1/4 -a + a^2)(1/2 - a) - (1/4 +a + a^2)(1/2 + a)

= (1/8 -a/2 + a^2/2 -a/4 + a^2 -a^3) - (1/8 +a/2 + a^2/2 +a/4 + a^2 + a^3)

= -a - a/2 - 2a^3

= (-3/2)a - 2a^3

Subtitusi a = 1/2.cos 2x

(-3/2)a - 2a^3

= (-3/2)(1/2.cos 2x) - 2(1/2.cos 2x)^3

= (-3/4)cos 2x - (1/4).(cos 2x)^3

Subtitusi x = 15

(-3/4)cos 2x - (1/4).(cos 2x)^3

= (-3/4)cos 30 - (1/4).(cos 30)^3

= (-3/4)(√3/2) - (1/4).(√3/2)^3

= (-3√3)/8 - (1/4)((3√3)/8)

= 3√3(-1/8 - 1/32)

= 3√3(-5/32)

= (-15√3)/32

sin^6 15 - cos^6 15 = (-15√3)/32