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}

Decimal Notation

0.86602 \dots

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

Use the Double Angle identity:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

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

Simplify

= cos (3 0^{\circ})

= cos (3 0^{\circ})

Use the following trivial identity:

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

cos (3 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{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