The answer to whether tan(21)=2tan(t) is False

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

p ro v e tan^{2} (x) + sin^{2} (x) = 1

p ro v e sin^{2} (θ) + cos^{2} (θ) = sec^{2} (θ)

p ro v e sin (x) - cos (x) + 1 = 0

p ro v e csc^{4} (x) = csc^{3} (x)

p ro v e tan^{2} (x) = sec^{2} (x) - sec (x) tan (x) + 1