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}

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 (4 5^{\circ})

Use the following trivial identity:

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