What is the value of sqrt(5+4tan(pi/4)) ?

The value of sqrt(5+4tan(pi/4)) is 3

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sqrt(5+4tan(pi/4))

5 + 4 tan (\frac{π}{4})

3

Solution steps

5 + 4 tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

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

= 5 + 4 \cdot 1

Simplify

5 + 4 \cdot 1 : 3

5 + 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= 5 + 4

Add the numbers:

5 + 4 = 9

= 9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= 3

arccos (- 0.9)

2 cos^{2} (\frac{π}{2})

\frac{tan ( 1 9 ^{\circ} ) + tan ( 4 7 ^{\circ} )}{1 - tan ( 1 9 ^{\circ} ) tan ( 4 7 ^{\circ} )}

arctan (\frac{- 3}{5})

cos (14 0^{\circ}) cos (2 0^{\circ}) - sin (14 0^{\circ}) sin (2 0^{\circ})