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

The value of cos(15)cos(15)-sin(15)sin(15) is (sqrt(3))/2

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

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

\frac{3}{2}

Solution steps

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

Simplify

= cos^{2} (1 5^{\circ}) - sin^{2} (1 5^{\circ})

Rewrite using trig identities:

cos (3 0^{\circ})

= cos (3 0^{\circ})

Use the following trivial identity:

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

= \frac{3}{2}

sin (\frac{1}{2} arctan (- \frac{5}{13}))

tan (- 0.01)

tan (\frac{5 π}{36})

arctan (\frac{100}{200})

arcsin (\frac{9}{12})

What is the value of cos(15)cos(15)-sin(15)sin(15) ?
The value of cos(15)cos(15)-sin(15)sin(15) is (sqrt(3))/2