SOLUTION: I am getting a bit confused as to what to do next on this this problem: Verify the identity by converting the left side into sines and cosines. (Simplify at each step.) cot(x)

Algebra ->  Trigonometry-basics -> SOLUTION: I am getting a bit confused as to what to do next on this this problem: Verify the identity by converting the left side into sines and cosines. (Simplify at each step.) cot(x)       Log On


   

Question 1206215: I am getting a bit confused as to what to do next on this this problem:
Verify the identity by converting the left side into sines and cosines. (Simplify at each step.)
cot(x) − tan(x) = sec(x)(csc(x) − 2 sin(x))
Here's what I have so far:
cot(x) − tan(x)= cos(x)/sin(x)-sin(x)/cos(x)
cos^2(x)-sin^2(x)/sin^2(x)cos(x) **The entire equation is over sin^2(x)cos^2(x)
I know that the top of the next equation would be:
1-(sin^2(x)+sin^2(x))
I'm not sure how to figure out the rest. Any help would be appreciated. Thank you!



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cot%28x%29+-+tan%28x%29+=+sec%28x%29%28csc%28x%29+-+2+sin%28x%29%29
left side
cot%28x%29+-+tan%28x%29....use identity cot%28x%29=cos%28x%29%2Fsin%28x%29+and tan%28x%29=sin%28x%29%2Fcos%28x%29

=cos%28x%29%2Fsin%28x%29-sin%28x%29%2Fcos%28x%29

=%28cos%5E2%28x%29-sin%5E2%28x%29%29%2F%28sin%28x%29%2Acos%28x%29%29....use identity cos%5E2%28x%29=1-sin%5E2%28x%29

=%281-sin%5E2%28x%29-sin%5E2%28x%29%29%2F%28sin%28x%29%2Acos%28x%29%29

=%281-2sin%5E2%28x%29%29%2F%28sin%28x%29%2Acos%28x%29%29...expand

=1%2F%28sin%28x%29%2Acos%28x%29%29-%282sin%5E2%28x%29%29%2F%28sin%28x%29%2Acos%28x%29%29...simplify

=%281%2Fsin%28x%29%29%2A%281%2Fcos%28x%29%29-2sin%28x%29%281%2Fcos%28x%29%29...use identity 1%2Fsin%28x%29=csc%28x%29+and 1%2Fcos%28x%29=sec%28x%29



=csc%28x%29+%2Asec%28x%29-%282sin%28x%29%29%28sec%28x%29%29...factor out+sec%28x%29

=sec%28x%29%28csc%28x%29+-2sin%28x%29%29