proof of double angle identity
Sine:
sin(2a) | = | sin(a+a) | ||
= | sin(a)cos(a)+cos(a)sin(a) | |||
= | 2sin(a)cos(a). |
Cosine:
cos(2a) | = | cos(a+a) | ||
= | cos(a)cos(a)+sin(a)sin(a) | |||
= | cos2(a)-sin2(a). |
By using the identity
sin2(a)+cos2(a)=1 |
we can change the expression above into the alternate forms
cos(2a)=2cos2(a)-1=1-2sin2(a). |
tan(2a) | = | tan(a+a) | ||
= | tan(a)+tan(a)1-tan(a)tan(a) | |||
= | 2tan(a)1-tan2(a). |
Title | proof of double angle identity |
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Canonical name | ProofOfDoubleAngleIdentity |
Date of creation | 2013-03-22 12:50:30 |
Last modified on | 2013-03-22 12:50:30 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 4 |
Author | drini (3) |
Entry type | Proof |
Classification | msc 51-00 |