Is 3tan^2(x)+13tan(x)=4 ?

The answer to whether 3tan^2(x)+13tan(x)=4 is False

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prove 3tan^2(x)+13tan(x)=4

prove

3 tan^{2} (x) + 13 tan (x) = 4

False

Solution steps

3 tan^{2} (x) + 13 tan (x) = 4

Show that the two sides are not equal

For

3 tan^{2} (x) + 13 tan (x) = 4

plug in

x = 0

3 tan^{2} (0) + 13 tan (0) = 0

3 tan^{2} (0) + 13 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

= 3 \cdot 0^{2} + 13 \cdot 0

Simplify

= 0

The two sides are not equal

\Rightarrow False

csc (\frac{π}{2} - θ) = sec (θ)

sin (x) cos (x) = cot (x)

\frac{sin ( a + 2 a ) + 4 sin ^{3} ( a )}{3} = sin (a)

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

cos (1 \cdot π) = - 1