# Find all solutions of the Equation

• November 27th 2008, 09:44 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
• November 27th 2008, 09:54 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
• November 27th 2008, 10:37 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) $\csc^2x-4=0$

$\csc^2 x=4$

$\csc x=\pm 2$

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

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

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

$\cos^2 x/2=1$

Can you proceed further?

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

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

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

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

Solve it...

4)Try to do this yourself as number 3 or else i will give further hints...
• November 27th 2008, 11:56 AM
running-gag
Just a small mistake in 3)
2 cos²x + cos x - 1 = 0 (Wink)
• November 27th 2008, 01:12 PM
ChargersFan84
Awesome. Thanks a bunch! I can take it from there.
• November 27th 2008, 07:58 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)