Is 3(tan(x))+sqrt(12)=sqrt(3) ?

The answer to whether 3(tan(x))+sqrt(12)=sqrt(3) is False

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prove 3(tan(x))+sqrt(12)=sqrt(3)

prove

3 (tan (x)) + 12 = 3

False

Solution steps

3 tan (x) + 12 = 3

Show that the two sides are not equal

For

3 tan (x) + 12 = 3

plug in

x = 0

3 tan (0) + 12 = 23 (Decimal : 3.46410 \dots)

3 tan (0) + 12

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 + 12

Simplify

3 \cdot 0 + 12 : 23

3 \cdot 0 + 12

3 \cdot 0 = 0

3 \cdot 0

Apply rule

0 \cdot a = 0

= 0

12 = 23

12

Prime factorization of

12 : 2^{2} \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

= 2^{2} \cdot 3

= 2^{2} \cdot 3

Apply radical rule:

= 3 2^{2}

Apply radical rule:

2^{2} = 2

= 23

= 0 + 23

0 + 23 = 23

= 23

= 23

The two sides are not equal

\Rightarrow False

Is 3(tan(x))+sqrt(12)=sqrt(3) ?
The answer to whether 3(tan(x))+sqrt(12)=sqrt(3) is False