Posted by Anonymous on Monday, February 20, 2012 at 6:50pm.
#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(90-x) = cosx
and cos(180-x) = -cosx , you are attempting to "prove" these in your solution
cosx-sin(90-x)sinx/cosx-cos(180-x)tanx
= cosx - cosx(tanx) - (-cosx)(tanx)
= cosx
I'm still confuse in #3
ok, let's go to your solution ....
from
cosx-(sin90cosx-cos90sinx)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-(sin90cosx-cos90sinx)sinx all over cosx-(cos180cosx+sin180sinx)tanx
sorry I should've put brackets to separate them.
[cosx-(sin90cosx-cos90sinx)sinx]/[cosx-(cos180cosx+sin180sinx)tanx]
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