Posted by **Mimi** on Tuesday, August 24, 2010 at 3:40am.

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

(/is square root sign

- trig -
**MathMate**, Tuesday, August 24, 2010 at 8:27am
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 -
**Reiny**, Tuesday, August 24, 2010 at 8:28am
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

## Answer This Question

## Related Questions

- Trig. - sec^2xcotx-cotx=tanx (1/cos)^2 times (1/tan)-(1/tan)=tan (1/cos^2) times...
- Math-Trigonometry - Show that if A, B, and C are the angles of an acute triangle...
- Trig - 4tan^2u-1=tan^2u 3tan^2u=1 tan^2u=1/3 sq. root of (tan^2u)=sq. root of (1...
- PreCalculus - Hi I need some assistance on this problem find the exact value do ...
- Trig - tan 15° using composite argument? - tan 15° tan (45°-30°) (tan 45° - tan ...
- trig - please help me. use trig. identities to find the exact value. tan 25° + ...
- trig - please help me. use trig. identities to find the exact value. tan 25° + ...
- Trigonometry - Find the exact value of tan(a-b) sin a = 4/5, -3pi/2<a<-pi...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Solving Trig equation - Solve the trig equation exactly in the interval 0≤...

More Related Questions