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gledanju0

gledanju0

Answered question

2022-06-21

Rearrange 3 tan 2 x sec x 1 = 0 to solve for x?
So far all I can do is rearrange it to form
3 sin 2 ( x ) cos ( x ) cos 2 ( x ) cos 2 ( x )
I don't know where to go from here or any other way to solve x

Answer & Explanation

Govorei9b

Govorei9b

Beginner2022-06-22Added 21 answers

You have a good start. From there you have
(1) 3 sin 2 ( x ) cos ( x ) cos 2 ( x ) cos 2 ( x ) = 0
which is equivalent to
(2) 3 sin 2 ( x ) cos ( x ) cos 2 ( x ) = 0
since any x such that cos x = 0 is not a solution of (2). Note that sin 2 x + cos 2 x = 1, so (2) becomes
3 cos x 4 cos 2 x = 0.
Mayra Berry

Mayra Berry

Beginner2022-06-23Added 7 answers

Hint: tan 2 x = sec 2 x 1 so you only have to solve a quadratic in the variable y = sec x.
Answer: x = sec 1 ( 1 ) or x = sec 1 ( 4 3 )

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