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}

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 (6 0^{\circ})

Use the following trivial identity:

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