What is the value of tan^2(45)-cos(30) ?

The value of tan^2(45)-cos(30) is 1-(sqrt(3))/2

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tan^2(45)-cos(30)

tan^{2} (4 5^{\circ}) - cos (3 0^{\circ})

1 - \frac{3}{2}

Decimal Notation

0.13397 \dots

Solution steps

tan^{2} (4 5^{\circ}) - cos (3 0^{\circ})

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 1^{2} - \frac{3}{2}

Simplify

= 1 - \frac{3}{2}

sin (- 5 0^{\circ})

cos (arctan (\frac{5}{12}) - arcsec (\frac{9}{7}))

tanh^{2} (1)

cos (- 8)

- arctan (\frac{\frac{30 + 20}{2}}{80})

What is the value of tan^2(45)-cos(30) ?
The value of tan^2(45)-cos(30) is 1-(sqrt(3))/2