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Last October 24, 2012, we did the derivation of Double Angle Formula. Right now, we will derive the formulas for Half Angle Formula from the formulas of Double Angle Formula.
Let's consider this one,
but
then the above equation becomes
If A = 2θ, then θ = ½ A
Take the square root on both sides of the equation,
Again, let's consider this one,
but
then the above equation becomes
If A = 2θ, then θ = ½ A
Take the square root on both sides of the equation,
How about for Tangent function? Well, let's derive for Tangent function. We know that
You can consider the above formula for Tangent function but there's a rule in Mathematics that the denominator must be free from radicals. Let's rationalize the denominator as follows:
