2006-10-29 04:44:06 · 4 answers · asked by biorob302 1 in Science & Mathematics ➔ Mathematics
this can be done simpler
numerator = cot y- tan y
= cos y/ sin y - sin y/cos y
= (cos^2y - sin^2y)/sin y cos y
(cos y+ sin y) (cos y - sin y)(sin y cos y)
so LHS
= (cos y- sin y)/ siny cos y = 1/sin y - 1/cos y
= cosec y - sec y
= RHS
=
2006-10-31 01:22:06 · answer #1 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
see ur precalc book, around chapter 5 there is a whold page of identities to help u solve this.
2006-10-29 12:46:58 · answer #2 · answered by dreamz 4 · 0⤊ 0⤋
cot y -tan y = cosy/siny - siny /cosy
= (cos^2y-sin^2y)/sinycosy
= (cosy+siny) (cosy-siny )/siny cosy
then coty-tany / siny +cosy = cosy-siny / sinycosy
= 1/siny - 1/cosy
= csc y - sec y
2006-10-29 13:14:23 · answer #3 · answered by grandpa 4 · 0⤊ 0⤋
Nr=coty-tany
=(cosy/siny)-(siny/cosy)
=(cos^2y-sin^2y)cosysiny
so (coty-tany)/(cosy+siny)
=[(cos^2y-sin^2y)/cosysiny]
/(cosy+siny)
=(cosy-siny)/cosysiny
=cosy/cosysiny - siny/cosysiny
=1/siny-1/cosy
=cscy-secy
hence proved
2006-10-29 12:51:17 · answer #4 · answered by raj 7 · 0⤊ 0⤋