goldenfuture5
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- Feb 20, 2009
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(sin x / 1+cos x) + (1+cos x/sin x)= 2csc x
Work and answer?
Work and answer?
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Solve proof: (sin x / 1+cos x) + (1+cos x/sin x)= 2csc x
- Thread starter goldenfuture5
- Start date
Re: Solve this proof!
(sin x / 1+cos x) + (1+cos x/sin x) means \(\displaystyle \frac{\sin x}{1}+\cos x+1+\frac{\cos x}{\sin x}\).
You need to learn to use parenthesis properly. I think you mean...
sin x /(1+cos x) + (1+cos x)/sin x which means \(\displaystyle \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}\).
If the latter is what you mean, just add the left side fractions together, then simplify the numerator. You will then see a use of the sin[sup:361220vp]2[/sup:361220vp]x + cos[sup:361220vp]2[/sup:361220vp]x = ??? identity. It will then easily simplify to get the right side.
(sin x / 1+cos x) + (1+cos x/sin x) means \(\displaystyle \frac{\sin x}{1}+\cos x+1+\frac{\cos x}{\sin x}\).
You need to learn to use parenthesis properly. I think you mean...
sin x /(1+cos x) + (1+cos x)/sin x which means \(\displaystyle \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}\).
If the latter is what you mean, just add the left side fractions together, then simplify the numerator. You will then see a use of the sin[sup:361220vp]2[/sup:361220vp]x + cos[sup:361220vp]2[/sup:361220vp]x = ??? identity. It will then easily simplify to get the right side.
goldenfuture5
New member
- Joined
- Feb 20, 2009
- Messages
- 4
Re: Solve this proof!
Yeah, I do mean the latter. Ok so right now I am at 2cos x = 2 all over sin x + sin x times cos x = 2csc x
I'm stuck now.
Yeah, I do mean the latter. Ok so right now I am at 2cos x = 2 all over sin x + sin x times cos x = 2csc x
I'm stuck now.
Re: Solve this proof!
\(\displaystyle \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{\sin x}{1+\cos x}\cdot \frac{\sin x}{\sin x}+\frac{1+\cos x}{\sin x}\cdot \frac{1+\cos x}{1+\cos x}=\frac{\sin^2x + (1+\cos x)^2}{\sin x(1+\cos x)}\).
Now, do some canceling and I leave the rest to you.
\(\displaystyle \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=\frac{\sin x}{1+\cos x}\cdot \frac{\sin x}{\sin x}+\frac{1+\cos x}{\sin x}\cdot \frac{1+\cos x}{1+\cos x}=\frac{\sin^2x + (1+\cos x)^2}{\sin x(1+\cos x)}\).
Now, do some canceling and I leave the rest to you.