prove tan(x)= 4/5

Solution

prove

tan (x) = \frac{4}{5}

False

Solution steps

tan (x) = \frac{4}{5}

Show that the two sides are not equal

For

tan (x) = \frac{4}{5}

plug in

x = 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

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

\frac{cot ^{2} ( t )}{cos ( t )} = cot (t) csc (t)

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

- csc^{2} (x) = - 1 - (cot (x))^{2}

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