Question

I need help with #6!

Answer 1

write everything in terms of sines and cosines, then algebra will get it

Answer 2

i know the cos is left alone & i need to do something with the inside of the parenthesis but things dont cancel out though>.<

Answer 3

what @Mertsj said

Answer 4

so i distribute the cos to all of them right?

Answer 5

& also to the bottom part of the fraction?

Answer 6

\[\cos(x)\left(\tan(x)+\cot(x)\right)=\csc(x)\] i find it a lot easier to replace \(\cos(x)\) by \(a\) and \(\sin(x)\) by \(b\) and do algebra with
\[a(\frac{b}{a}+\frac{a}{b})\] and see if we can turn this in to \(\frac{1}{b}\)

Answer 7

help?

Answer 8

the algebra part is
\[a(\frac{b}{a}+\frac{a}{b})=b+\frac{a^2}{b}\] now add them up get \[\frac{b^2+a^2}{b}\]

Answer 9

now comes the only trig step
\[\frac{\sin^2(x)+\cos^2(x)}{\sin(x)}\] and guess what you get in the numerator?