Sin^2x-cos2x=0!!!!!!!!!

Question

pls help for test?

Answer 1

sin²x - cos2x = 0

Recall : Trigonometry identities cos2x = 1-2sin²x

Substitute cos2x = 1- 2sin²x in the above trigonometry equation

sin^2x -(1 - 2sin²x) = 0

sin^2x - 1 + 2sin²x = 0

3sin²x - 1 = 0

Add 1 to each side

3sin²x = 1

sin²x = 1 / 3

Take square root to each side

sinx = 1 / √3

Take arcsin to each side

arcsin(sinx) = arcsin(1 / √3)

x = arcsin(1 / √3).