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:
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

  1. Reiny

    #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

  2. Anonymous

    I'm still confuse in #3

  3. Reiny

    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

  4. Anonymous

    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]

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Pre-Calc

    Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 - cosx)/cosx)/((sinx …
  2. Simplifying with Trigonometry Identities

    Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each other. …
  3. Trigonometry.

    ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! Generally these are done by changing everything to sines and cosines, unless you see some obvious identities. Also generally, it is best to start with the more complicated side …
  4. Trig........

    I need to prove that the following is true. Thanks (cosx / 1-sinx ) = ( 1+sinx / cosx ) I recall this question causing all kinds of problems when I was still teaching. it requires a little "trick" L.S. =cosx/(1-sinx) multiply top and …
  5. maths - trigonometry

    I've asked about this same question before, and someone gave me the way to finish, which I understand to some extent. I need help figuring out what they did in the second step though. How they got to the third step from the second. …
  6. Math 12

    Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/sinx+cosx = cscxtanx/sinx+cosx Is the correct answer cscxtanx/sinx+cosx?
  7. Trigonometry Check

    Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [cosx-(sin90cosx-cos90sinx)sinx]/[cosx-(cos180cosx+sinx180sinx)tanx] = [cosx-((1)cosx-(0)sinx)sinx]/[cosx-((-1)cosx+(0)sinx)tanx] = [cosx-cosxsinx]/[cosx+cosxtanx] = [cosx(1-sinx]/[cosx(1+tanx] …
  8. Trigonometry

    Prove the following trigonometric identities. please give a detailed answer because I don't understand this at all. a. sin(x)tan(x)=cos(x)/cot^2 (x) b. (1+tanx)^2=sec^2 (x)+2tan(x) c. 1/sin(x) + 1/cos(x) = (cosx+sinx)(secx)(cscx) d. …
  9. Calculus

    Q: If y=sinx/(1+tanx), find value of x not greater than pi, corresponding to maxima or minima value of y. I have proceeded thus- Equating dy/dx=0 we get{ (1+tanx)cosx-sinx.sec^2 x}/(1+tanx)^2=0……..(A) Or cosx+sinx=sinx.sec^2 x …
  10. Precalculus/Trig

    I can't seem to prove these trig identities and would really appreciate help: 1. cosx + 1/sin^3x = cscx/1 - cosx I changed the 1: cosx/sin^3x + sin^3x/sin^3x = cscx/1-cosx Simplified: cosx + sin^3x/sin^3x = cscx/1-cosx I don't know …

More Similar Questions