Hi, do any of you know how to solve this problem?

Find the only value of x in that satisfies the equation

The answer was , but I don't know how it came to that answer.

Thanks!

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- Nov 9th 2011, 07:39 PMjigogwapo16Solve for x that Satisfies the Trigonometric Equation
Hi, do any of you know how to solve this problem?

Find the only value of x in that satisfies the equation

The answer was , but I don't know how it came to that answer.

Thanks! - Nov 9th 2011, 08:04 PMTKHunnyRe: Solve for x that Satisfies the Trigonometric Equation
First, I'm tempted to change to csc(x) and sec(x), but like many, maybe I'm not all that comfortable with those two functions.

Second, I'm tempted to multiply by sin(x), since sin(x) is never zero in the given interval. Maybe I'm lots more familar with the tangent function.

Third, maybe I'm tempted to get rid of the cosines by the Pythagorean Identity.

Not sure right off. What have you tried? - Nov 9th 2011, 08:18 PMDevenoRe: Solve for x that Satisfies the Trigonometric Equation
i think fractions are evil. i try to get rid of them.

- Nov 9th 2011, 10:47 PMjigogwapo16Re: Solve for x that Satisfies the Trigonometric Equation
I'm actually pretty stumped in this problem. This was actually a problem in the national round of one of the math contests here in our country.

The first thing I did was that I ignored the interval I would have as the answer, since and . But then I saw the friggin' interval restriction, and I got lost. - Nov 9th 2011, 11:08 PMjigogwapo16Re: Solve for x that Satisfies the Trigonometric Equation
- Nov 10th 2011, 01:49 AMsbhatnagarRe: Solve for x that Satisfies the Trigonometric Equation

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Expressing the equation in terms of cos(x):

.

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Let . Equation becomes:

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Factorising:

.

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This is not the only solution to x. Let us also solve .

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Let us finalize our answer:

Can you find the value of x in that satisfies the equation using the general solution from the second factor?

- Nov 10th 2011, 08:13 PMjigogwapo16Re: Solve for x that Satisfies the Trigonometric Equation