Proving the Double-Angle Formulas (Grades 11-12)

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Proving the Double-Angle Formulas

1. 
Prove that [math]sin(2theta) = 2sin(theta)cos(theta)[/math].






2. 
Prove that [math]cos(2theta) = cos^2(theta) - sin^2(theta)[/math].






3. 
Given that [math]cos(2theta) = cos^2(theta)- sin^2(theta)[/math], prove that [math]cos(2theta) = 2cos^2(theta)-1[/math].






4. 
Given that [math]cos(2theta) = cos^2(theta)-sin^2(theta)[/math], prove that [math]cos(2theta) = 1-2sin^2(theta)[/math].






5. 
Prove that [math]tan(2theta) = (2tan(theta))/(1-tan^2(theta))[/math].






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