Question

Buktikan bahwa sin⁴x - cos⁴x = 1-2 cos²x

Answer 1

Pertama gunakan bntuk selisih kuadrat :
a^2 - b^2 = (a+b)(a-b),
lalu gunakan identitas :
sin^2 x + cos^2 x= 1
so,
sin^4 x - cos^4 x = (sin^2 x)^2 - (cos^2)^2
= (sin^2 x + cos^2 x)(sin^2 x - cos^2 x)
= 1 * (sin^2 x- cos^2 x)
= sin^2 x - cos^2 x
= 1 - cos^2 x - cos^2 x
= 1 - 2cos^2 x