SOLUTION: i must show that sin0=cos0tan0. how do i go about doing this. please help.

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Question 287845: i must show that sin0=cos0tan0. how do i go about doing this. please help.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Let o = opposite
Let a = adjacent
Let h = hypotenuse
Let T = any angle.

Formula you want to prove is:

sin(T) = cos%28T%29%2ATan%28T%29

sin(T) = o%2Fh

cos(T) = a%2Fh

tan(T) = o%2Fa

sin(T) = cos%28T%29%2ATan%28T%29+ becomes:

o%2Fh = a%2Fh+%2A+o%2Fa

This is equivalent to:

o%2Fh = %28a%2Ao%29%2F%28a%2Ah%29

The a in the numerator and the a in the denominator cancel out so the equation becomes:

o%2Fh = o%2Fh

Since this is true, then the formulas are equivalent confirming that:

o%2Fh = %28a%2Ao%29%2F%28h%2Aa%29 which is the same as:

o%2Fh = %28a%2Fh%29%2A%28o%2Fa%29 which is the same as:

sin(T) = cos%28T%29%2Atan%28T%29