What is the value of cos(22)cos(23)-sin(22)sin(23) ?

The value of cos(22)cos(23)-sin(22)sin(23) is (sqrt(2))/2

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cos(22)cos(23)-sin(22)sin(23)

cos (2 2^{\circ}) cos (2 3^{\circ}) - sin (2 2^{\circ}) sin (2 3^{\circ})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (2 2^{\circ}) cos (2 3^{\circ}) - sin (2 2^{\circ}) sin (2 3^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ})

cos (2 2^{\circ}) cos (2 3^{\circ}) - sin (2 2^{\circ}) sin (2 3^{\circ})

Use the Angle Sum identity:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

= cos (2 2^{\circ} + 2 3^{\circ})

Simplify

= cos (4 5^{\circ})

= cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 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}

3 cos^{2} (π)

(sin (1 5^{\circ}) + sin (7 5^{\circ}))^{6}

sin (\frac{17 π}{12}) + sin (\frac{13 π}{12})

2 cos (\frac{π}{2}) + sin (\frac{π}{2})

cos (- \frac{7 π}{2})

What is the value of cos(22)cos(23)-sin(22)sin(23) ?
The value of cos(22)cos(23)-sin(22)sin(23) is (sqrt(2))/2