Pythagorean Identities: Sum and Difference: cos 0 + sin 0 = 1 1 + tan 0 = sec2 0 sin(A + B) = sin A cos B + sin B cos A cot2 0 + 1 = csc2 0 cos( A + B) = sin A sin B F cos A cos B Half-Angle Formulas: Double-Angle Formulas: sin- 0 = 1 - cos (20) sin (20) = 2 sin A cos e 2 cos (20) = cos2 0 - sin2 0 cos' 0 = 1 + cos( 28) 2 =1 - 2 sin2 0 = 2cos- 0 - 1 Antiderivatives: sec 0 tan 0 de = sec e + C sec e de = In | sec e + tan #| + C' sec2 0 de = tan 0 + C' csco cot 0 de = - csce + C csco de = - In | csce + cot #| + C csc2 0 de = - cot # + C Questions For each of the following problems, always start with drawing an appropriate right triangle for trigonometric substitution. 1. Set up, but do not evaluate, an appropriate trigonometric integral for the following integrals. 7-3 (a) V1+ x2 ( b ) V9 - 12 (c ) (9 - 4x2)3/2 dac