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

The value of cos(45)cos(15) is (sqrt(3)+1)/4

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cos(45)cos(15)

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

\frac{3 + 1}{4}

Solution steps

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

Rewrite using trig identities:

\frac{cos ( 3 0 ^{\circ} ) + cos ( 6 0 ^{\circ} )}{2}

= \frac{cos ( 3 0 ^{\circ} ) + cos ( 6 0 ^{\circ} )}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

= \frac{\frac{3}{2} + \frac{1}{2}}{2}

Simplify

\frac{\frac{3}{2} + \frac{1}{2}}{2} : \frac{3 + 1}{4}

= \frac{3 + 1}{4}

tan (- 16 5^{\circ})

cot (39 0^{\circ})

6 cos (\frac{π}{6})

sec^{2} (2)

arccos (sin (\frac{11 π}{6}))

What is the value of cos(45)cos(15) ?
The value of cos(45)cos(15) is (sqrt(3)+1)/4