Solve the equation on the interval [0,2pi ) sin^2 x-cos^2 x=0

Bernard Boyer

Bernard Boyer

Answered question

2022-07-25

Solve the equation on the interval [ 0 , 2 π )
sin 2 x cos 2 x = 0

Answer & Explanation

bardalhg

bardalhg

Beginner2022-07-26Added 15 answers

( 1 cos 2 x ) cos 2 x = 0
1 2 cos 2 x = 0
2 cos 2 x = 1
cos 2 x = 1 2
cos x = ± 1 2 = ± 2 2
x = π 4 , 3 π 4 , 5 π 4 , 7 π 4
stylaria3y

stylaria3y

Beginner2022-07-27Added 1 answers

sin 2 x ( 1 sin 2 x ) = 0, use trig identity
2 sin 2 x = 1
sin x = ± 2 2 , s o   x = π 4 , 3 π 4
x = π 4 + n π 2
and x = 3 π 4 + n π 2

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