Is tan^2(pi/4)=tan(pi/4) ?

The answer to whether tan^2(pi/4)=tan(pi/4) is True

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prove tan^2(pi/4)=tan(pi/4)

prove

tan^{2} (\frac{π}{4}) = tan (\frac{π}{4})

True

Solution steps

tan^{2} (\frac{π}{4}) = tan (\frac{π}{4})

Manipulating left side

tan^{2} (\frac{π}{4})

Simplify

tan^{2} (\frac{π}{4}) : 1

tan^{2} (\frac{π}{4})

Simplify

tan (\frac{π}{4}) : 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

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}

= 1

= 1^{2}

Apply rule

1^{a} = 1

= 1

= 1

Manipulating right side

tan (\frac{π}{4})

Simplify

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

sec (A) - tan (A) = \frac{cos ( A )}{1 + sin ( A )}

(cos (θ) + sin (θ))^{2} = 1 + 2 cos (θ) sin (θ)

sin^{2} (θ) = \frac{3}{4} sin (θ) - \frac{1}{4} sin (3 θ)

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