# Trigonometric equations

Find the value of x (in degrees) for:

cos(6x+5) = 1/sec(4x+15)

sec(2x+6)*cos(5x+3)=1.

See the attached file.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Here are some hints:

sec(x)=1/cos(x)

Now when we say cos(a)=cos(b)

it is not sufficient to conclude a=b

You must remember that

cos(a)=cos(b)=cos(b+360)=cos(b+720)=cos(b+360n)

this is true for any trigonometric function.

Each triginometric function has also parity characteristics. It can be either even f(x)=f(-x)

or odd f(-x)=-f(x)

cosine is an even function, thus we gen another possibility for the equation:

cos(a)=cos(b)=cos(-b)=cos(360-b)=cos(720-b)=cos(360n-b)

So we have infinite number of possible solutions to the equations that come in pairs for any integer number n. Make sure you account for all of them.

If you get stuck, you can look at the attached solutions.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:06 pm ad1c9bdddf>https://brainmass.com/math/trigonometry/trigonometric-identities-periodicity-28179