# Homework Help: Simplify math issue

1. Feb 21, 2010

### PanTh3R

1. The problem statement, all variables and given/known data
simplify:
$$\sin\theta\sec\theta+\cos\theta\csc\theta$$

2. Relevant equations
Reciprocal identities, Quotient identities, Pythagorean identities

3. The attempt at a solution

$$\sin\theta\sec\theta+\frac{1}{\sec\theta}\frac{1}{\sin\theta}$$

$$\sin\theta\sec\theta+\frac{1}{\sin\theta\sec\theta}$$

and this is where i get stuck...can i get help from anyone?

2. Feb 21, 2010

### tiny-tim

Hi PanTh3R!

(have a theta: θ )

You need to be systematic …

keep all the sin and cos, get rid of the sec and csc.

Try again.

3. Feb 21, 2010

### PanTh3R

Re: simplify

so i get....

$$\sin\theta\frac{1}{\cos\theta}+cos\theta\frac{1}{\sin\theta}$$

then i put each in one fraction right?

$$\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}$$

to

$$\tan\theta+cot\theta$$

is that the simplest it can get?

4. Feb 21, 2010

### tiny-tim

Hi PanTh3R!

This is elementary algebra …

put both fractions over the same denominator (the LCM).

5. Feb 21, 2010

### PanTh3R

Re: simplify

im sorry im really bad with these i just started doing them um so i do

$$\frac{\sin^2\theta+\cos\theta}{\cos\theta\sin\theta}$$

i still don't get it wont that make it more complicated?

6. Feb 21, 2010

### tiny-tim

Bottom right, top wrong.

7. Feb 21, 2010

### PanTh3R

Re: simplify

would it be....

$$\frac{\sin^2\theta+\cos^2\theta}{\cos\theta\sin\theta}$$

then

$$\frac{1-\cos^2+\cos^2\theta}{\cos\theta\sin\theta}$$

into

$$\frac{1}{\cos\theta\sin\theta}$$

i feel so frustrated sry

8. Feb 21, 2010

### Bohrok

Re: simplify

Looks like that's the simplest you can get it.

9. Feb 22, 2010

### icystrike

Re: simplify

$$2cosec(2\theta)$$ would seems better.

10. Feb 22, 2010

### Mentallic

Re: simplify

It depends if the OP has been exposed to double-angles yet. Trigonometric simplifications of this form are commonly taught before the student ever learns that $2sin\theta cos\theta=sin(2\theta)$

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