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

Bernard Boyer 2022-07-25 Answered
Solve the equation on the interval [ 0 , 2 π )
sin 2 x cos 2 x = 0
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Answers (2)

bardalhg
Answered 2022-07-26 Author has 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
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stylaria3y
Answered 2022-07-27 Author has 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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