What is the value of cos(10)cos(35)-sin(10)sin(35) ?

The value of cos(10)cos(35)-sin(10)sin(35) is (sqrt(2))/2

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cos(10)cos(35)-sin(10)sin(35)

cos (1 0^{\circ}) cos (3 5^{\circ}) - sin (1 0^{\circ}) sin (3 5^{\circ})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (1 0^{\circ}) cos (3 5^{\circ}) - sin (1 0^{\circ}) sin (3 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ})

cos (3 5^{\circ}) cos (1 0^{\circ}) - sin (3 5^{\circ}) sin (1 0^{\circ})

Use the Angle Sum identity:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

= cos (3 5^{\circ} + 1 0^{\circ})

Simplify

= cos (4 5^{\circ})

= cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

= \frac{2}{2}

cos^{2} (3 2^{\circ})

- e^{- 0} cos (0) - e^{- 0} sin (0)

4 sin (\frac{7 π}{4})

arccot (- \frac{1}{3})

cot (\frac{17 π}{3})

What is the value of cos(10)cos(35)-sin(10)sin(35) ?
The value of cos(10)cos(35)-sin(10)sin(35) is (sqrt(2))/2