Trigonometry

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:
cosx-sin(90-x)sinx/cosx-cos(180-x)tanx
= cosx-(sin90cosx-cos90sinx)sinx/cosx-(cos180cosx+sinx180sinx)tanx
= cosx-sin90cosx+cos90sinxsinx/cosx-cos180cosx-sinx180sinxtanx
= cosx-sin90cosx+cos90sin^2x/cosx-cos180cosx-sinx180sinxtanx
= ???

What do I do next?

Please help and Thank you

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  1. #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

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  2. I'm still confuse in #3

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  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

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  4. 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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