Question 1144497: Prove the identities of cot^2 - cos^2=cot^2cos^2
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
The general rule is to change the appearance of the expression on one side of the equation until it looks like the other side.
For this example, leave the expression on the right unchanged.
On the left side...
(1) Write each cot^2 as (cos^2)/(sin^2)
(2) Get a common denominator
(3) Factor out the common factor in the numerator
(4) Use sin^2+cos^2=1 to rewrite the numerator
The result will be the expression on the right.
Comments....
(1) Unless you have a lot of experience with trig functions, it is nearly always easiest to write sec, csc, tan, and cot in terms of sin and cos
(2) The identity sin^2+cos^2=1 (in one form or another -- e.g., 1-cos^2 = sin^2) is used in proving identities ten times as often as all other trig identities together
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