Is tan(θ)=sqrt(tan(θ)+2) ?

The answer to whether tan(θ)=sqrt(tan(θ)+2) is False

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prove tan(θ)=sqrt(tan(θ)+2)

prove

tan (θ) = tan (θ) + 2

False

Solution steps

tan (θ) = tan (θ) + 2

Show that the two sides are not equal

For

tan (θ) = tan (θ) + 2

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

tan (0) + 2 = 2 (Decimal : 1.41421 \dots)

tan (0) + 2

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 + 2

Simplify

= 2

The two sides are not equal

\Rightarrow False

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