SOLUTION: sinxtanx=secx-cosx

Question 230137: sinxtanx=secx-cosx
Found 2 solutions by algebrapro18, Theo:
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Well to do this problem we need to remember a few facts:
1) sec(x) = 1/cos(x)
2) sin^2(x) = 1-cos^2(x)
3) tan(x) = sin(x)/cos(x)
Okay now to prove this identity we need to work with one side to see if we can get the other.
left hand side:
sinxtanx
= sinx(sinx/cosx)by number 3.
= sin^2x/cosx
= (1-cos^2x)/cosx by number 2.
= 1/cosx - cos^2x/cosx
= secx - cosx by number 1.
There now we found that the left hand side equals the right hand side and we're done. Just to show you that it doesn't matter what side we choose I'm going to work with the right hand side and get the left hand side as well.
Right hand side:
secx-cosx
=1/cosx - cosx by 1.
=(1-cos^2x)/cosx
=sin^2x/cosx by 2.
=sinx/cosx * sinx
=tanxsinx by 3.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Your expression is

Since , your expression becomes:

This becomes:

Since , this means that:

Replace in your expression with this to get:

Since , you can replace cos(x) in your equation to get:

This is the same as:

because .

Your expression has become:

Remove parentheses to get:

Since , you can replace in your equation to get:

Simplify to get:

Since this is what you wanted to prove, you're done.

Note I am showing sin^2(x) as sin(x)^2 because it doesn't come out good on the formula rendering routine with sin^2(x).

Example:

sin^2(x) shows up as

sin(x)^2 shows up as

The second version is technically incorrect but it shows up clearer so I used it.

Note that sin(x) * sin(x) really is (sin(x))^2 but I shortened it to sin(x)^2 to eliminate all those extra parentheses that muddied up the presentation.

Just remember that sin(x)^2 is the same as sin^2(x) and we'll be ok.

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