trig

posted by .

Given that tan 45=1, use tan(x+y) to show that tan 22.5= /2 - 1.
(/is square root sign

  • trig -

    tan(x+y)=(tan(x)+tan(y))/(1-tan(x)tan(y))

    substitute x=y to get
    tan(2x) = 2tan(x)/(1-tan²(x))
    Substitute tan(2x)=1 and solve for tan(x).
    Reject the negative root knowing that tan(x)≥0 for 0<x<π/2.

  • trig -

    tan(x+y) = (tanx + tany)/(1 - tanxtany)

    so tan 45
    = tan(22.5 + tan22.5)/(1 - tan22.5tan22.5)
    = 2tan22.5)/1 - tan^2 22.5)
    let tan22.5 = y for ease of typing

    1 = 2y/(1 - y^2)
    1 - y^2 = 2y
    y^2 + 2y - 1 = 0
    y^2 + 2y = 1 , by completing the square
    y^2 + 2y + 1 = 1+1
    (y+1)^2 = 2
    y+1 = √2
    y = √2-1

    tan22.5° = √2 - 1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
  2. Trig - tan 15° using composite argument?

    tan 15° tan (45°-30°) (tan 45° - tan 30°)/1+ tan 45°tan30° (1-√3/3)/(1+1√3/3) then i donnt what to do/ chancel out. Can someone finish it if i didn't get it wrong. thanks in advance
  3. Trig.

    sec^2xcotx-cotx=tanx (1/cos)^2 times (1/tan)-(1/tan)=tan (1/cos^2) times (-2/tan)=tan (-2/cos^2tan)times tan=tan(tan) sq. root of (-2/cos^2)= sq. root of (tan^2) sq. root of (2i)/cos=tan I'm not sure if I did this right. If I didn't, …
  4. Trig

    4tan^2u-1=tan^2u 3tan^2u=1 tan^2u=1/3 sq. root of (tan^2u)=sq. root of (1/3) tanu=sq. root of (3)/3 tanu=sq. root of 1 Did I do this one right?
  5. PreCalculus

    Hi I need some assistance on this problem find the exact value do not use a calculator cot[(-5pi)/12] Here is my attempt RT = square root pi = 3.14... cot[(-5pi)/12]={tan[(-5pi)/12]}^-1={tan[(2pi)/12-(8pi)/12]}^-1={tan[pi/6-(2pi)/3]}^-1={(tan[pi/6]-tan[(2pi)/3])/(1+tan[pi/6]tan[(2pi)/3])}^-1={((RT[3])/3+RT[3])/(1+((RT[3])/3)(-RT3))}^-1 …
  6. trig

    please help me. use trig. identities to find the exact value. tan 25° + tan 5° / 1- tan 25° tan 5°
  7. trig

    please help me. use trig. identities to find the exact value. tan 25° + tan 5° / 1- tan 25° tan 5°
  8. Trigonometry

    Find the exact value of tan(a-b) sin a = 4/5, -3pi/2<a<-pi; tan b = -sqrt2, pi/2<b<pi identity used is: tan(a-b)=(tan a-tan b)/1+tan a tan b simplify answer using radicals. (a is alpha, b is beta)
  9. Math-Trigonometry

    Show that if A, B, and C are the angles of an acute triangle, then tan A + tan B + tan C = tan A tan B tan C. I tried drawing perpendiculars and stuff but it doesn't seem to work?
  10. Pre-Cal

    Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. (tan(74°)-tan(14°))/(1+tan(74°)tan(14°)) =__________ Find it's exact value (not decimal form) =__________ Note: A similar …

More Similar Questions