i think i ve da best ans for ur ques
its a shortcut
0 to pie / 2 ki limits hai so dis shortcut is applicable on sin (ki power n) x as well as for cos ( ki power n) x
sin ^ 8 x = ( 7 . 5 . 3 .1 / 8 . 6 . 4 . 2 . )* pie / 2 since da power is even ie. 8 so v'll multiply by pie / 2
& iff power of sin x is odd then we ll not multiply by pie/ 2
its a short cut applicable only if limits r b/w 0 to pie / 2