SOLUTION: Use tan2θ= sin2θ/cos2θ to prove the double angle formula for tangent: tan2θ= 2tanθ/1-tan^2(theta) can someone please help me with this equation and explain
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Question 980781: Use tan2θ= sin2θ/cos2θ to prove the double angle formula for tangent: tan2θ= 2tanθ/1-tan^2(theta) can someone please help me with this equation and explain it to me? Thank you.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
See the lesson Addition and subtraction formulas in this site,
section "Proof of the addition and subtraction formulas for tangents".
Or, below is a direct derivation.
We have
= , (1)
according to the definition of tangents as the ratio of sines and cosines.
Next,
= . (2)
This is the formula for sines of the double argument. Similarly,
= . (3)
This is the formula for cosines of the double argument.
Now, substitute (2) and (3) into the numerator and the denominator of (1). You will get
= . (4)
Now, divide the numerator and denominator in the right side of (4) by . You will get
= . (5)
As a last step, replace the ratio by in (5). You will get
= . (6)
This is what has to be proved. You finally got the formula you needed.
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