Is tan^2(x/2)+2tan(x/2)-5=3tan(x/2) ?

The answer to whether tan^2(x/2)+2tan(x/2)-5=3tan(x/2) is False

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prove tan^2(x/2)+2tan(x/2)-5=3tan(x/2)

prove

tan^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2}) - 5 = 3 tan (\frac{x}{2})

False

Solution steps

tan^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2}) - 5 = 3 tan (\frac{x}{2})

Show that the two sides are not equal

For

tan^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2}) - 5 = 3 tan (\frac{x}{2})

plug in

x = 0

tan^{2} (\frac{0}{2}) + 2 tan (\frac{0}{2}) - 5 = - 5

tan^{2} (\frac{0}{2}) + 2 tan (\frac{0}{2}) - 5

Rewrite using trig identities:

tan (\frac{0}{2}) = 0

tan (\frac{0}{2})

Simplify

= 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

= 0^{2} + 2 \cdot 0 - 5

Simplify

= - 5

3 tan (\frac{0}{2}) = 0

3 tan (\frac{0}{2})

Rewrite using trig identities:

tan (\frac{0}{2}) = 0

tan (\frac{0}{2})

Simplify

= 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

= 3 \cdot 0

Simplify

= 0

The two sides are not equal

\Rightarrow False

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

\frac{cot ( x ) + 2}{csc ( x )} = 2 sin (x) + cos (x)

(sec (x)) (sin (x)) = tan (x)

tan (2 x) = 2 sin (x) cos (x) sec (2 x)

sin^{3} (z) cos^{2} (z) = sin^{3} (z) - sin^{5} (z)

Is tan^2(x/2)+2tan(x/2)-5=3tan(x/2) ?
The answer to whether tan^2(x/2)+2tan(x/2)-5=3tan(x/2) is False