What is the value of (2tan(22.5))/(1-tan^2(22.5)) ?

The value of (2tan(22.5))/(1-tan^2(22.5)) is 1

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(2tan(22.5))/(1-tan^2(22.5))

\frac{2 tan ( 22. 5 ^{\circ} )}{1 - tan ^{2} ( 22. 5 ^{\circ} )}

1

Solution steps

\frac{2 tan ( 22. 5 ^{\circ} )}{1 - tan ^{2} ( 22. 5 ^{\circ} )}

Rewrite using trig identities:

tan (4 5^{\circ})

\frac{2 tan ( 22. 5 ^{\circ} )}{1 - tan ^{2} ( 22. 5 ^{\circ} )}

Use the Double Angle identity:

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = tan (2 x)

= tan (2 \cdot 22. 5^{\circ})

Simplify

= tan (4 5^{\circ})

= tan (4 5^{\circ})

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

arctan (\frac{14}{12})

cos^{2} (- 6 0^{\circ})

arctan (\frac{43}{74})

30 cos (3 7^{\circ})

sin (6) π^{\circ}

What is the value of (2tan(22.5))/(1-tan^2(22.5)) ?
The value of (2tan(22.5))/(1-tan^2(22.5)) is 1