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lobht98

lobht98

Answered question

2022-06-14

Solve cos 2 x sin x + 1 = 0 for 0 x 360
In my attempts I've been substituting 1 2 sin 2 x in place of cos 2 x and I've tried to work it out from there but haven't really got anywhere.

Answer & Explanation

Christina Ward

Christina Ward

Beginner2022-06-15Added 19 answers

Your attempt to use the following identity is a good one:
cos ( 2 x ) 1 2 sin 2 x
Then, you obtain the following:
1 2 sin 2 x sin x + 1 = 2 sin 2 x sin x + 2 = 0
The trick here is to substitute u = sin x , and this gives a quadratic equation:
2 u 2 u + 2 = 0 2 u 2 + u 2 = 0
You can now use the quadratic formula.

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