Question

QUESTION 18 Use the substitution z = tan(x/2) to evaluate the integral / 3-cos e de ОА. tan-1 ( ✓2 tan 2 --()) +C OB. tan tan +C V2 OC V2 tan 2 Etan () )+c 2 OD. 1 tan tan +C 2 OE. tan V2 tan +C 2

Answer 1

Solution - 3 + caso uring trignometic identity it tomtex) = see²x - I sec? ( 442) dx (tom (A) +2) Substitute tem (2/2) see 2(0/2) z = da dn 2 1 :d2 T = z2+2 w Agin substitute u= Z 52 du = d2 HW

es du au²+2 du 52 u²+1 2 w uring stone and integral Sur du I du = Tom (4) therefore -IS Tom'u u &c indo substitution u- Z ㅜ 7 Tam" ( 3 ) te 11 -IS Again undo substitution Z= tem (*%2) al Ia I Tomi d2 tem (2/2) 2 1-)) tc Aue 1 xf2 tem (2/2) I= Ix + B 52 z da rom' (1 + x 2 tem + "(ml I- 52 Tom 12 tem tom (al (2/2))+ +C 2 2 option c Aug