2007-11-21 11:41:59 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
tan(A+B) = (tanA + tanB) / (1 - tanAtanB)
If A+B
tan(2A) = 2tan(A) / (1 - tan²A)
tan(π/4) = 2tan(π/8) / (1 - tan²(π/8))
1 = 2tan(π/8) / (1 - tan²(π/8))
tan(π/8) = x
Note: π/8 is in the first quadrant so tan(π/8)>0. x>0
1 = 2x/(1-x²)
1-x² = 2x
x² + 2x - 1 = 0
x = [-2±sqrt(2²+4)]/2
= [-2±2sqrt(2)]/2
= -1±sqrt(2)
x>0
x = sqrt(2) - 1
tan(π/8) = sqrt(2) - 1
2007-11-21 11:52:14 · answer #1 · answered by gudspeling 7 · 2⤊ 0⤋
Half-angle.
tan((pi/4/)2)
2007-11-21 11:45:09 · answer #2 · answered by Amelia 6 · 1⤊ 1⤋
Use the half angle formula.
tan(x/2) = sinx / (1 + cosx)
For the question at hand we have:
tan(π/8) = sin(π/4) / [1 + cos(π/4)]
tan(π/8) = (1/√2) / [1 + (1/√2)] = 1/(√2 + 1)
tan(π/8) = 1*(√2 - 1) / [(√2 + 1)(√2 - 1)]
tan(π/8) = (√2 - 1) / (2 - 1) = (√2 - 1) / 1 = √2 - 1
2007-11-21 11:58:08 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
Hint:
tan(2x)=2tan(x)/(1-tan(x)^2)
Substitute pi/8 for x and solve for tan(x).
2007-11-21 11:46:14 · answer #4 · answered by moshi747 3 · 1⤊ 0⤋
PI/8=22.5 degress.
Do you have a calculator?
tan(pi/8)=0.4142
2007-11-21 11:49:34 · answer #5 · answered by cidyah 7 · 1⤊ 5⤋