# Thread: How do I simplify these things?!

1. ## How do I simplify these things?!

Big numbers like the 2 are to the power of:

1. tan x * cos x

2.csc x *cos x * tan x
3. (1 - sin x) (1 + sin x)
4. sin x + cos x * tan x
5. cos2x-1
_____________
cos2x
6.cos x * sin x * 1
___
csc x

2. I'll help you get started but you can do the full simplifications.

1. $\displaystyle \tan{x} \times\cos{x} = \frac{\sin{x}}{\cos{x}} \times \cos{x} = \sin{x}$

2. $\displaystyle \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\cos{x}} \times \frac{\sin{x}}{\cos{x}} \times \cos{x}$

3. $\displaystyle \frac{1-\sin{x}}{1+\sin{x}} = \frac{(1-\sin{x})^2}{1-\sin^2{x}} = \frac{(1-\sin{x})^2}{\cos^2{x}}$

4. $\displaystyle = \sin{x} + \sin{x} = 2\sin{x}$

5. $\displaystyle \frac{\cos^2{x} - 1}{\cos^2{x}} = \frac{1 - \sin^2{x} - 1}{\cos^2{x}} = -\frac{\sin^2{x}}{\cos^2{x}} = -\tan^2{x}$

6. $\displaystyle \cos{x} \times \sin{x} \times \csc{x} = \cos{x} \times \sin{x} \times \frac{1}{\sin{x}}$

3. Originally Posted by nzmathman
I'll help you get started but you can do the full simplifications.

1. $\displaystyle \tan{x} \times\cos{x} = \frac{\sin{x}}{\cos{x}} \times \cos{x} = \sin{x}$

2. $\displaystyle \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\cos{x}} \times \frac{\sin{x}}{\cos{x}} \times \cos{x}$

3. $\displaystyle \frac{1-\sin{x}}{1+\sin{x}} = \frac{(1-\sin{x})^2}{1-\sin^2{x}} = \frac{(1-\sin{x})^2}{\cos^2{x}}$

4. $\displaystyle = \sin{x} + \sin{x} = 2\sin{x}$

5. $\displaystyle \frac{\cos^2{x} - 1}{\cos^2{x}} = \frac{1 - \sin^2{x} - 1}{\cos^2{x}} = -\frac{\sin^2{x}}{\cos^2{x}} = -\tan^2{x}$

6. $\displaystyle \cos{x} \times \sin{x} \times \csc{x} = \cos{x} \times \sin{x} \times \frac{1}{\sin{x}}$
------------------------------------------------------------------
2. $\displaystyle \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\sin{x}} \times \cos{x} \times \frac{\sin{x}}{\cos{x}}$ = ?

4. the two cos's cancel out and then the two sin's cancel out so the answer is one

5. Originally Posted by j0nath0n3
------------------------------------------------------------------
2. $\displaystyle \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\sin{x}} \times \cos{x} \times \frac{\sin{x}}{\cos{x}}$ = ?

$\displaystyle \csc{x}= \frac{1}{\sin{x}}$ not $\displaystyle \frac{1}{\cos{x}}$