What is the value of cos(45)cos(15)-sin(45)sin(15) ?

The value of cos(45)cos(15)-sin(45)sin(15) is 1/2

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cos(45)cos(15)-sin(45)sin(15)

cos (4 5^{\circ}) cos (1 5^{\circ}) - sin (4 5^{\circ}) sin (1 5^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

cos (4 5^{\circ}) cos (1 5^{\circ}) - sin (4 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ})

cos (4 5^{\circ}) cos (1 5^{\circ}) - sin (4 5^{\circ}) sin (1 5^{\circ})

Use the Angle Sum identity:

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

= cos (4 5^{\circ} + 1 5^{\circ})

Simplify

= cos (6 0^{\circ})

= cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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{1}{2}

= \frac{1}{2}

tan^{2} (4 5^{\circ} - \frac{35}{2})

cot (- \frac{11 π}{3})

sin (2 \frac{π}{6})

sin (arcsin (- \frac{1}{53}))

arctan (\frac{22}{30})

What is the value of cos(45)cos(15)-sin(45)sin(15) ?
The value of cos(45)cos(15)-sin(45)sin(15) is 1/2