Help sec^4X- sec^2X = 1/cot^4X + 1/cot^2X

I assume the 10x2 means 10 squared. (I will show it as 10x**2)
(22x+11)(10x**2+5x) factors into"
11(2x+1)*5(2x**2+1x)
=55(2x+1)(2x**2+1x)
=(55x)(2x+1)(2x+1)
Multiplied out, it becomes 55x(4x**2+4x+1)
= 220x**3 + 220x**2 + 55x

csc(x)=1/sin(x)
sec(x)=1/cos(x)
csc(x)/sec(x)=(1/sin(x))*(cos(x)=cot(x)
csc(x)*cot(x)/sec(x)=(cot(x))^2=(tan(x))^(-2)

x equals 1

First multiply the numbers outside the parentheses by what is inside the parentheses, which results in:

6 - 2x + 3x - 3 = 4x

then combine what you can:

6 - 3 = 3,
-2x + 3x = 1x

which leaves:

3 + x = 4x

Subtract the x on the left from the 4x on the right and you get:

3 = 3x

Divide by 3 to get the x alone

3 / 3 = 1

x = 1

SEC, CSC & COT are the INVERSE of COS, SIN & TAN and are usually require hitting the "2nd F" or "Func" key of the calc to make:

SIN button work as COSEC,

COS button work as SEC

TAN button work as COT

Formulas are below:

sec x = 1
cos x

cosec x = 1
sin x

cot x = 1 = cos x
tan x sin x

Good luck!

We can write this polynomial as:

• (x-(-2))*(x-1)*(x-3)=
• (x+2)(x-1)(x-3)=
• (x+2)[x*(x-3)-1*(x-3)]=
  
• (x+2)*(x^2-3x-x+3)=
• (x+2)(x^2-4x+3)=
• x*(x^2-4x+3)+2*(x^2-4x+3)=
• x^3-4x^2+3x+2x^2-8x+6=
• x^3-2x^2-5x+6

x^3-2x^2-5x+6 is polynomial with roots -2, 1, 3.

You can see this polynomial in following picture:



Notice that it intersects x axis for x=-2, 1 and 3 (because these are roots of polynomial).

4x-(2x-3)=0
=>4x-2x+3=0 ; (after the bracket's oepned and multiplied by - [minus])
=>2x+3=0 ; taken x as common and 4-2=2 i.e. x(4-2) = 2x
=>2x=-3 ; +3's moved on the right-hand side, so it becomes -3
=>x=-3/2 ; 2 has been moved to the right-hand side and divided with -3 i.e 1/2 multiplied by -3 = -3/2

Hence, x = -3/2


Good luck.

Thanks for using FixYa.

Hi,
This calculator does not have a Solve function or a solver. However this example of yours is very simple that you can do it by hand. If you do not mind I will show you how to solve it. Not everything needs a calculator.
You want to solve for x. OK

1. Start by gathering similar terms 4x-x =3x; -13+5 =-8
   
2. Rewrite your equation as 3x+1=2x-8
3. Make the +1 change side while changing its sign
   
4. 4x+1 -1 = 2x-8 -1 or 4x=2x-9
5. Make +2x on the Right hand side go to the left hand side, changing its sign in the process 4x-2x=-9 or 2x=-9
6. Divide both members by 2. This gives
   
7. x=-9/2 or -4.5 if a decimal result is required.

Hope it helps.

According to these mobo specs that board will do AGP 2X up to 533MB / sec and AGP 4X up to 1066MB/sec.

Here is the link to your mobo manual.

http://www.fixya.com/support/p25279-dfi_ad73_pro_motherboard/manual-33795

Hi,

Let's say your 3 numbers are a, b and c. Because they are consecutive and odd, you can write them like this:

a = 2x-1, b = 2x+1, c = 2x+3

Now, your problem looks like this:

2(2x-1)(2x+1) = (2x+1)(2x+3) + 7
2(4x^2-1) = 4x^2+6x+2x+3 + 7
8x^2-2 = 4x^2+8x+10
4x^2-8x-12 = 0
4(x^2-2x-3) = 0
x^2-2x-3 = 0

The solutions for this quadratic equation ( see more about this kind of equations here: http://en.wikipedia.org/wiki/Quadratic_equation ) are x=3 or x=-1. So, you've got two sets of solutions:

[1] a = 5, b = 7, c = 9
[2] a = -3, b = -1, c = 1


Take care,
Alex

I shall attempt :D
1) cosec A + cot A = 3
we know that (cot A)^2 + 1 = (cosec A)^2
Hence, (cosec A)^2 - (cot A)^2 = 1
thus, (cosec A + cot A) (cosec A - cot A) = 1
3 (cosec A - cot A) = 1
(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3
(cosec A + cot A) = 3
Summing them, 2 cosec A = 3 1/3
cosec A = 6 2/3 = 5/3
sin A = 0.15
Thus, cos A = sqrt (1 - (sin A)^2) = 0.989


2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2
expand
LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x
We can calculate that
tan x cosec x = sec x (since tan x = sin x / cos x)
sec x cot x = cosec x
so the above is
LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x
LHS = 2 + cot x + tan x - sec x cosec x
LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)
LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)
LHS = 2 (proved)