Trig/Precal 2 Please help
\[\frac{ 1+cosu }{ sinu } + \frac{ sinu }{ cosu+1 }\]
So far I have this: \[\frac{ (1+sinu)^2 + \sin^2u }{ (cosu+1)(sinu) }\] \[\frac{ \sin^2u+2sinu+1+\sin^2u }{ (cosu+1)(sinu) }\]
I'm supposed to Simplify the trigonometric expression.by the way.
You are correct in believing that the least common denominator of these two fractions is (sin u)(cos u + 1). But I see problems with your numerators. Would you mind multiplying out (1 + cos u)(1 + cos u)? Please multiply: (sin u)(sin u). Write your results here, please.
\[ \frac{\cos (u)+1}{\sin (u)}+\frac{\sin (u)}{\cos (u)+1}=\\\frac{\sin ^2(u)+(\cos (u)+1)^2}{\sin (u) (\cos (u)+1)}=\\\frac{\sin ^2(u)+\cos ^2(u)+2 \cos (u)+1}{\sin (u) (\cos (u)+1)}= \] Can you finish it now?
What is \[ \sin^2(u) + \cos^2(u) \]
\[ \frac{\sin ^2(u)+\cos ^2(u)+2 \cos (u)+1}{\sin (u) (\cos (u)+1)}=\\\frac{2 \cos (u)+2}{\sin (u) (\cos (u)+1)}=\frac{2}{\sin (u)}=2 \csc (u) \]
OOH I messed up on the top part, its supposed to be (1+cos^u)^2 Thanks eliassa. You too mathmale. Thanks guys
YW
Your showing your work helped me help you. Glad you're making progress!
Wish I could have gave you both medals haha.
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