Common Trig Identity Derivations

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SUMMARY

The discussion focuses on the derivation of common trigonometric identities, specifically sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos²(θ) - sin²(θ), and sin²(θ) = (1 - cos(2θ))/2. The user seeks online resources for step-by-step explanations of these derivations. The simplest method involves using the angle addition formulas: cos(A+B) = cosAcosB - sinAsinB and sin(A+B) = sinAcosB + sinBcosA, with A set equal to B for simplification.

PREREQUISITES
  • Understanding of basic trigonometric functions and identities
  • Familiarity with angle addition formulas in trigonometry
  • Basic algebra skills for manipulating equations
  • Knowledge of the unit circle and its properties
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Students studying trigonometry, educators teaching trigonometric concepts, and anyone looking to deepen their understanding of trigonometric identities and their derivations.

david martin
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I'm looking for a source online that gives the step by step derivation of common trig identities, such as sin(2theta) = 2sin(theta)cos(theta), cos(2theta) = cos2(theta)-sin2(theta), sin2(theta) = (1 - cos(2theta))/2, ect. I did do 20 minuntes or so of searching online, nothing was exactly what I was hoping for. Is there a website explaining the derivations or should I fork out the $100 for a trig text? Thanks
 
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The simplest way uses the these identities:

cos(A+B)= cosAcosB - sinAsinB

and sin(A+B) = sinAcosB + sinBcosA

then put A=B. Proving the above identities might prove to be a bit more difficult.
 

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