# Find all solutions of the Equation

• Nov 27th 2008, 08:44 AM
ChargersFan84
Find all solutions of the Equation
Any help would be appreciated for these problems. Thanks in advance

csc(squared)x-4=0

sec x/2 = cos x/2

2sin(squared)x-cosx=1

3sec(squared)x+4cos(squared)x=7
• Nov 27th 2008, 08:54 AM
running-gag
Quote:

Originally Posted by ChargersFan84
2sin(squared)x-cosx=1

You mean 2sin²x-cosx=1 ?
In this case just change sin²x by 1-cos²x and solve the second degree equation in cosx
• Nov 27th 2008, 09:37 AM
great_math
Quote:

Originally Posted by ChargersFan84

1)csc(squared)x-4=0

2)sec x/2 = cos x/2

3)2sin(squared)x-cosx=1

4)3sec(squared)x+4cos(squared)x=7

1) $\displaystyle \csc^2x-4=0$

$\displaystyle \csc^2 x=4$

$\displaystyle \csc x=\pm 2$

For what value of x does $\displaystyle \csc x$ has $\displaystyle 2$ or $\displaystyle -2$ as its value?

2) $\displaystyle \sec x/2=\cos x/2$

$\displaystyle \frac 1{\cos x/2}=\cos x/2$

$\displaystyle \cos^2 x/2=1$

Can you proceed further?

3)$\displaystyle 2\sin^2-\cos x=1$

$\displaystyle 2(1-\cos^2 x)-\cos x=1$

$\displaystyle 2-2\cos^2 x-\cos x=1$

$\displaystyle 2\cos^2 x+\cos x-1=0$

Solve it...

4)Try to do this yourself as number 3 or else i will give further hints...
• Nov 27th 2008, 10:56 AM
running-gag
Just a small mistake in 3)
2 cos²x + cos x - 1 = 0 (Wink)
• Nov 27th 2008, 12:12 PM
ChargersFan84
Awesome. Thanks a bunch! I can take it from there.
• Nov 27th 2008, 06:58 PM
great_math
Quote:

Originally Posted by running-gag
Just a small mistake in 3)
2 cos²x + cos x - 1 = 0 (Wink)

Sorry...

I was asleep (Sleepy) at that time..(Headbang)