Solving Trigonometric Identities (A bit Hard)

[cmhabs94]

Alright, well I am having a difficult time getting these equations to equal out! I keep hitting trouble and have hit a road block.

Here is the problem...

csc(x)+cot(x) = cot(x)csc(x)
tan(x)+sin(x)

I am just going to work on the LEFT PART of the equation.

1 + cos(x)
sin(x) sin(x)
ALL OVER
sin(x) + sin(x)
cos(x)

so...
1 + cos(x) / sin(x) * cos(x) / sin(x) + sin(x)cos(x)

simplifying the bold leads to...

1 + cos(x) / sin(x) * cos(x) / sin(x)(1+cos(x))

I am stuck here, particular getting the common denominator and then simplyfing it out to equal cot(x)csc(x)

Any help would be appreciated, thanks.

 

[SHScanuck]

Hello,
I believe you are on the right track with this solving trigonometric identities.

(1+Cos(x))/Sin(x) * Cos(x)/(Sin(x) + Sin(x)Cos(x))

Factor out the Sin(x) on the bottom and cancel the (1+Cos(x)) term (Top and Bottom)

(1+Cos(x))/Sin(x) * Cos(x)/(Sin(x)*(1+Cos(x))

thus,

1/Sin(x) * Cos(x)/Sin(x) = CSC(x)COT(x)

 

[cmhabs94]

Thank you so much! I kept going over that problem for about 30 mins; so focused on getting a common denominator that I forget to cross cancel! Ahh, I hate stupid mistakes.

Thanks,
- C