SOLUTION: Help is super appreciated :) Establish the identity: {{{(csc(x)cos(x))/(csc(x)-sin(x))=sec(x)}}} (cscx*cosx)/(cscx-sinx)=secx

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Question 1154792: Help is super appreciated :)
Establish the identity:

(cscx*cosx)/(cscx-sinx)=secx
Found 3 solutions by rothauserc, MathLover1, Edwin McCravy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
(csc(x) * cos(x))/(csc(x) -sin(x)) = sec(x)
:
Note csc(x) = 1/sin(x), sec(x) = 1/cos(x)
:
Work on the left side of the = sign
:
(cos(x)/sin(x)) / (((1/sin(x)) - sin(x)) =
:
(cos(x)/sin(x)) / ((1 - sin^2(x))/sin(x)) =
:
(cos(x)/sin(x)) * (sin(x)/(1 - sin^2(x)) =
:
cos(x)/cos^2(x) =
:
Note cos^2(x) = 1 - sin^2(x)
:
1/cos(x) = sec(x)
:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


manipulate left side
.......use identity: and

=

= .........

=

= .........

=

=

=


Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!

 

We'll work with the left side.

 

Multiply top and bottom by sin(x)

 

Cancel the sin(x)'s on top, distribute on the bottom:

 

Cancel the sin(x)'s in the first term on the bottom:







Cancel the cos(x) into the cos²(x)







Edwin
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