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Double Angle Formulas

Double Angle Formulas. s in 2A = 2 sin A cos A cos 2A = cos 2 A – sin 2 A c os 2A = 2 cos 2 A – 1 c os 2A = 1 – 2 sin 2 A t an 2A = 2 tan A 1 – tan 2 A. sin 2x = sin ( x + x ) = sinx cosx + cosx sinx = 2 sinx cosx.

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Double Angle Formulas

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  1. Double Angle Formulas

  2. sin 2A = 2 sin A cos A • cos 2A = cos2 A – sin2 A • cos 2A = 2 cos2 A – 1 • cos 2A = 1 – 2 sin2 A • tan 2A = 2 tan A 1 – tan2 A

  3. sin 2x = sin ( x + x ) = sinxcosx + cosxsinx = 2 sinxcosx

  4. cos 2x = cos2x – sin2x • = ( 1 – sin2x ) – sin2x • = 1 – 2 sin2x • = cos2x – ( 1 – cos2x • = 2cos2x - 1

  5. Verify the Identity: • sec 2x = cos²x + sin²x • cos²x - sin²x

  6. 1 = 1 • cos 2x cos 2x

  7. cos A - sin A = cos 2AcosA + sin A

  8. Cross-multiply:(cosA-sinA)(cosA+sinA)=cos2Acos²A-sin²A = cos 2Acos 2A = cos 2A

  9. tan 1/2 A = sin A 1 + cos A

  10. 1 - cos A = sin A sin A 1 + cos Across-multiply:1 - cos²A = sin² A sin² A = sin² A

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