What is the value of (2tan(105))/(1-tan^2(105)) ?

The value of (2tan(105))/(1-tan^2(105)) is (sqrt(3))/3

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(2tan(105))/(1-tan^2(105))

\frac{2 tan ( 10 5 ^{\circ} )}{1 - tan ^{2} ( 10 5 ^{\circ} )}

\frac{3}{3}

Solution steps

\frac{2 tan ( 10 5 ^{\circ} )}{1 - tan ^{2} ( 10 5 ^{\circ} )}

Rewrite using trig identities:

tan (3 0^{\circ})

= tan (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

= \frac{3}{3}

- sin (2 \frac{π}{12}) \cdot 2

cos (5 \cdot \frac{π}{2})

sin (4 5^{\circ}) + sin (4 5^{\circ})

arcsin (\frac{1}{1.25})

arctan (sec (0))

What is the value of (2tan(105))/(1-tan^2(105)) ?
The value of (2tan(105))/(1-tan^2(105)) is (sqrt(3))/3