SOLUTION: Sec(x)-cos(x)=sin(x)tan(x) Prove Thank you!

Algebra ->  Geometry-proofs -> SOLUTION: Sec(x)-cos(x)=sin(x)tan(x) Prove Thank you!      Log On


   

Question 1151814: Sec(x)-cos(x)=sin(x)tan(x)
Prove
Thank you!
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
First step can be

1%2Fcos%28x%29-cos%28x%29=sin%28x%29tan%28x%29
Now see far far you can go.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


sec%28x%29-cos%28x%29+=+sin%28x%29%2Atan%28x%29

You need to make the left hand side look like the right hand side, or make the right hand side look like the left hand side.

Since there is an addition on the left hand side and a multiplication on the right hand side, it is probably easier to leave the right hand side alone and work with the left hand side.

The first step undoubtedly is to express sec(x) in terms of sin(x) and/or cos(x).

%281%2Fcos%28x%29%29-cos%28x%29+=+sin%28x%29%2Atan%28x%29

About the only thing you can do with the left hand side is combine the terms with a common denominator.

1%2Fcos%28x%29-%28cos%28x%29%5E2%29%2Fcos%28x%29+=+sin%28x%29%2Atan%28x%29

%281-cos%28x%29%5E2%29%2Fcos%28x%29+=+sin%28x%29%2Atan%28x%29

I leave it to you to finish from there....

Note that in working problems like this, you will use these identities at least 10 times as often as all the others together:

sin%28x%29%5E2%2Bcos%28x%29%5E2+=+1
sin%28x%29%5E2+=+1-cos%28x%29%5E2
cos%28x%29%5E2+=+1-sin%28x%29%5E2