10. (5.4) In this problem, we Will evaluate common trigonometric integrals involving pow ers of sin($) and cos(ac) and products such as sin(m$) cos(nac). Our main tools will be usubstitution and the following trig identities: 1 (I) sin2(x) + cos2(m) : 1 (IV) sin(mac) cos(n$) : [sin((m + n)ac) + sin((m n)x)] (II) sin2(m) 2 i280\" (V) sin(mm) sin(m:) = %[cos((m + n)m) cos((m n)5r;)] 1 + cos(2:c) 1 (III) cos2(3:) : (VI) cos(m:c) cos(n:c) : [cos((m + n)zv) + cos((m n)m)] 2 Sin2(:t)cl:c using (II). sin3(:1:)cl3: using (I) and usubstitution with \"(37) : COS(33'). Start by writing / (b) [8111(456) cos(5:c)da: using (IV). / / sin3(3:)d:2: = / 5mm) sin(:1:)d:2: and replace Si2($) with 1 (3082(zt) from (I). (d) / 0085(33)d:2: using (I) and usubstitution With u(:2:) = 8111(93). Start by writing / COS5(:L')d:c : cosam)? sin(a:)dm and replace 0082(16) with 1 Sin2(a:) from (I). (e) / 0082(33)Sin3(3:)d:t using (I) and usubstitution with 7.1.(33) = 008(33). Start by writing / 0052a) sin3(:c)d:t = f 005%.) mm) sin(3:)da: and replace sin2(:c) with 1 0082(113) from (I)