Posted by **Anonymous** on Monday, February 20, 2012 at 6:50pm.

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

- Trigonometry -
**Reiny**, Monday, February 20, 2012 at 7:44pm
#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

- Trigonometry -
**Anonymous**, Monday, February 20, 2012 at 7:50pm
I'm still confuse in #3

- Trigonometry -
**Reiny**, Monday, February 20, 2012 at 7:57pm
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

- Trigonometry -
**Anonymous**, Monday, February 20, 2012 at 8:08pm
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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