What is the value of 2cos^2(67.5)-1 ?

The value of 2cos^2(67.5)-1 is -(sqrt(2))/2

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2cos^2(67.5)-1

2 cos^{2} (67. 5^{\circ}) - 1

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

2 cos^{2} (67. 5^{\circ}) - 1

Rewrite using trig identities:

cos (13 5^{\circ})

2 cos^{2} (67. 5^{\circ}) - 1

Use the Double Angle identity:

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

= cos (2 \cdot 67. 5^{\circ})

Simplify

= cos (13 5^{\circ})

= cos (13 5^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\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{2}{2}

= - \frac{2}{2}

sin (35 0^{\circ})

arccos (sin (\frac{2 π}{3}))

sin^{2} (0.5)

arctan (\frac{2 π}{3})

arcsin (\frac{5}{3})

What is the value of 2cos^2(67.5)-1 ?
The value of 2cos^2(67.5)-1 is -(sqrt(2))/2