SOLUTION: I want to know the prove on double angle identities, Please explain with detail step by step and give examples. please help me, i need it thank you.

Question 809977: I want to know the prove on double angle identities,
Please explain with detail step by step and give examples. please help me, i need it thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I want to know the prove on double angle identities,
------
Since sin(a+b) = sin(a)cos(b)+cos(a)sin(b),
sin(2x) = sin(x+x) = sin(x)cos(x)+cos(x)sin(x) = 2sin(x)cos(x)
-----
Since cos(a-b) = cos(a)cos(b)-sin(a)sin(b)
cos(2x) = cos(x+x) = cos(x)cos(x)- sin(x)sin(x) = cossin^2(x)-cos^2(x)
-----
tan(2x) = sin(2x)/cos(2x)
-----
= [2sin(x)cos(x)]/[cos^2(x)-sin^2(x)]
Divide numerator and denominator by cos^2(x) to get:
= 2tan(x)/(1-tan^2(x))
==============
Cheers,
Stan H.
==============
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