Double Angle Formulas

sin 2x = sin ( x + x ) = sinx cosx + cosx

sinx = 2 sinx cosx

cos 2x = cos2x – sin2x

= ( 1 – sin2x ) – sin2x= 1 – 2 sin2x

= cos2x – ( 1 – cos2x = 2cos2x - 1

Verify the Identity:

sec 2x = cos²x + sin²x cos²x - sin²x

1 = 1

cos 2x cos 2x

cos A - sin A = cos 2A cosA + sin A

Cross-multiply:(cosA-sinA)

(cosA+sinA)=cos2Acos²A-sin²A = cos 2A

cos 2A = cos 2A

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

1 - cos A = sin A sin A 1 + cos A

cross-multiply:1 - cos²A = sin² A sin² A = sin² A