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}

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 (6 0^{\circ})

Use the following trivial identity:

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