SOLUTION: prove
Sin(90-θ)/sec(90- θ)*tan(90- θ)/cos θ=cos θ
Algebra.Com
Question 212096: prove
Sin(90-θ)/sec(90- θ)*tan(90- θ)/cos θ=cos θ
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Note: In order to use the Algebra.com's software more effectively, I am going to use "x" instead of "θ".
Often the easiest way to prove identities is to use basic identities to convert all other trig functions into sin and/or cos. So we will start by replacing sec and tan using and :
To simplify this compound fraction, all we need to do is multiply the top and bottom of the "big" fraction by cos(90- x):
Now we can cancel the cos(90-x)'s:
leaving
Since sin(90-x) = cos(x) we can substitute:
We can cancel a cos(x):
leaving
Note: This is just one way to prove this identity. There are many others.
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