prove tan(θ)= 1/3

Solution

prove

tan (θ) = \frac{1}{3}

False

Solution steps

tan (θ) = \frac{1}{3}

Show that the two sides are not equal

For

tan (θ) = \frac{1}{3}

plug in

θ = 0

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= 0

The two sides are not equal

\Rightarrow False

csc^{4} (x) (cot^{2} (x)) = csc^{4} (x)

\frac{csc ^{2} ( o )}{1 + tan ^{2} ( o )} = cot^{2} (o)

\frac{sin ^{2} ( x )}{cos ^{2} ( x )} + 1 = sec^{2} (x)

cos^{2} (x) tan^{2} (2 x) = sin^{2} (x)

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