prove tan(21)=2tan(t)

Solution

prove

tan (2 1^{\circ}) = 2 tan (t)

False

Solution steps

tan (2 1^{\circ}) = 2 tan (t)

Show that the two sides are not equal

For

tan (2 1^{\circ}) = 2 tan (t)

plug in

t = 0

tan (2 1^{\circ}) = 0.38386 \dots

tan (2 1^{\circ})

Refine to a decimal form

= 0.38386 \dots

2 tan (0) = 0

2 tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

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}

= 0

= 2 \cdot 0

Simplify

= 0

The two sides are not equal

\Rightarrow False

tan^{2} (x) + sin^{2} (x) = 1

\frac{cos ( θ ) - cos ( 5 θ )}{sin ( θ ) + sin ( 5 θ )} = tan (2 θ)

sin^{2} (θ) + cos^{2} (θ) = sec^{2} (θ)

sin (x) - cos (x) + 1 = 0

(1 - cos (θ)) (csc (θ) + cot (θ)) = sin (θ)