Trigonometry
posted by Anonymous .
Simplify #1:
cscx(sin^2x+cos^2xtanx)/sinx+cosx
= cscx((1)tanx)/sinx+cosx
= cscxtanx/sinx+cosx
Is the correct answer cscxtanx/sinx+cosx?
Simplify #2:
sin2x/1+cos2X
= ???
I'm stuck on this one. I don't know what I should do.
Simplify #3:
cosxsin(90x)sinx/cosxcos(180x)tanx
= cosx(sin90cosxcos90sinx)sinx/cosx(cos180cosx+sinx180sinx)tanx
= cosxsin90cosx+cos90sinxsinx/cosxcos180cosxsinx180sinxtanx
= cosxsin90cosx+cos90sin^2x/cosxcos180cosxsinx180sinxtanx
= ???
What do I do next?
Please help and Thank you

#1
(1/sinx)(sin^2x + cos^2x(sinx/cosx) )/(sinx + cosx)
= (sinx + cosx)/(sinx+cosx)
= 1
#2
sin 2x/(1+ cos 2x)
= 2sinxcosx/(1 + 2sin^2x  1)
= 2sinxcosx/2cos^2x
=sinx/cosx
= tan x
#3 new approach
remember that sin(90x) = cosx
and cos(180x) = cosx , you are attempting to "prove" these in your solution
cosxsin(90x)sinx/cosxcos(180x)tanx
= cosx  cosx(tanx)  (cosx)(tanx)
= cosx 
I'm still confuse in #3

ok, let's go to your solution ....
from
cosx(sin90cosxcos90sinx)sinx/cosx(cos180cosx+sinx180sinx)tanx
= cosx((1)cosx(0)sinx)(tanx)  ((1)cosx+(0)sinx)tanx
= cosx  cosxtanx + cosxtanx
= cosx 
I know where you're getting at but it's cosx(sin90cosxcos90sinx)sinx all over cosx(cos180cosx+sin180sinx)tanx
sorry I should've put brackets to separate them.
[cosx(sin90cosxcos90sinx)sinx]/[cosx(cos180cosx+sin180sinx)tanx]