What is the value of cos(15)cos(75)+sin(15)sin(75) ?

The value of cos(15)cos(75)+sin(15)sin(75) is 1/2

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cos(15)cos(75)+sin(15)sin(75)

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Rewrite using trig identities:

cos (6 0^{\circ})

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

Use the Angle Difference identity:

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

= cos (1 5^{\circ} - 7 5^{\circ})

Simplify

= cos (- 6 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 6 0^{\circ}) = cos (6 0^{\circ})

= 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}

arctan (\frac{- 1}{- 3})

sin (3 0^{\circ}) \cdot cos (3 0^{\circ})

tan^{4} (\frac{π}{4})

sin (- 63 0^{\circ})

sin (- 34 5^{\circ})

What is the value of cos(15)cos(75)+sin(15)sin(75) ?
The value of cos(15)cos(75)+sin(15)sin(75) is 1/2