Trigonometry equation tan ⁡ 2 x + 3 sec ⁡ x + 3 = 0...

rzfansubs87

rzfansubs87

Answered

2022-07-07

Trigonometry equation tan 2 x + 3 sec x + 3 = 0 for tan 2 x + 3 sec x + 3 = 0

Answer & Explanation

Zackery Harvey

Zackery Harvey

Expert

2022-07-08Added 21 answers

Clearly, cos 2 x cos x 0
Multiply both sides of the given equation
cos x sin 2 x + 3 ( 1 + cos x ) cos 2 x = 0
0 = 2 sin x cos 2 x + 3 ( 1 + cos x ) cos 2 x
= 4 sin x 2 cos x 2 cos 2 x + 3 2 cos 2 x 2 cos 2 x
= 2 cos x 2 ( 2 sin x 2 cos 2 x + 3 cos x 2 cos 2 x )
If cos x 2 = 0 , x 2 = ( 2 n + 1 ) 90 x = ( 2 n + 1 ) 180 180 ( mod 360 )
Else 2 sin x 2 cos 2 x + 3 cos x 2 cos 2 x = 0
2 tan x 2 = 3 ( 2 cos 2 x 1 ) cos 2 x
Use cos x = 1 tan 2 x 2 1 + tan 2 x 2 which unfortunately leaves us with a bi-quadratic equation in tan x 2

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