Prove trig Identity - C3

Need help with this, I don't know where to start.

\frac{\cot \ x - \cos \ x}{ 1 - \sin \ x} \equiv \cot \ x

Reply 1

megeggan

try 1/tanx= cotx= cosx/sinxfor the left hand side

Reply 2

tiny hobbit

uer23

Need help with this, I don't know where to start.

\frac{\cot \ x - \cos \ x}{ 1 - \sin \ x} \equiv \cot \ x

Put cot x as cos x/sin x then multiply top and bottom of the whole fraction by sin x to get rid of the double layer fractions then factorise and look out for some brackets to cancel.

General principle - if you have a mixture of functions, putting them into sines and cosines is often good. (Why would you not use this technique if tan^2 x and sec^2 x were involved?)

Reply 3

Low Profile

With Cotx you can either use 1/tanx or cosx/sinx rule of indentities... I would use the second one : )

Reply 4

uer23

Thanks for the help guys, I've been able to solve it.

Reply 5

uer23

tiny hobbit

Why would you not use this technique if tan^2 x and sec^2 x were involved?

I don't know, why is that ?

Reply 6

tiny hobbit

Because of the identity tan^2 x + 1 = Sec^2 x so you can convert one of these into the other. Usually that will be simpler than putting it all into sines and cosines.