Solve the Equation sin 2x+ sqrt(3)cos 2x=1

acapotivigl

acapotivigl

Answered question

2022-09-12

Solve the Equation
sin 2 x + 3 cos 2 x = 1

Answer & Explanation

Theodore Dyer

Theodore Dyer

Beginner2022-09-13Added 10 answers

sin 2 x + 3 cos 2 x 1 = 0
2 sin x cos x + 3 cos 2 x 3 sin 2 x sin 2 x cos 2 x = 0
2 sin x cos x cos 2 x + 3 cos 2 x cos 2 x 3 sin 2 x cos 2 x sin 2 x cos 2 x cos 2 x cos 2 x = 0
2 t g x + 3 3 t g 2 x t g 2 x 1 = 0
3 t g 2 x + t g 2 x 2 t g x + 1 3
t g 2 x ( 3 + 1 ) 2 t g x + ( 1 3 ) = 0
t g x = 0
t 2 ( 3 + 1 ) 2 t + ( 1 3 ) = 0
D = 4 4 ( 1 + 3 ) ( 1 3 ) = 4 4 ( 1 3 ) = 4 + 8 = 12
D = 12 = 2 3
t 1 = 2 + 2 3 2 ( 3 + 1 ) = 1
t 2 = 2 2 3 2 ( 3 + 1 ) = 2 ( 1 3 ) 2 ( 1 + 3 ) = ( 1 3 ) ( 1 3 ) ( 1 + 3 ) ( 1 3 ) = ( 1 3 ) 2 1 3 =
= 1 2 3 + 3 2 = 4 2 3 2 = 3 2
t g x = 1
x = π 4 + π n
t g x = 3 2
x = a r c t g ( 3 2 ) + π k
Bordenauaa

Bordenauaa

Beginner2022-09-14Added 18 answers

sin 2 x + 3 cos 2 x = 1
R = ( 1 ) 2 + ( 3 ) 2 = 4 = 2
1 2 sin 2 x + 3 2 cos 2 x = 1 2
cos π 6 sin 2 x + sin π 6 cos 2 x = 1 2
sin ( π 6 + 2 x ) = 1 2
π 6 + 2 x = ( 1 ) n π 6 + π n
x = ( 1 ) n π 12 + π n 2 π 12

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