What is the value of cos(160)cos(40)+sin(160)sin(40) ?

The value of cos(160)cos(40)+sin(160)sin(40) is -1/2

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cos(160)cos(40)+sin(160)sin(40)

cos (16 0^{\circ}) cos (4 0^{\circ}) + sin (16 0^{\circ}) sin (4 0^{\circ})

- \frac{1}{2}

Solution steps

cos (16 0^{\circ}) cos (4 0^{\circ}) + sin (16 0^{\circ}) sin (4 0^{\circ})

Rewrite using trig identities:

cos (12 0^{\circ})

= cos (12 0^{\circ})

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

= - \frac{1}{2}

0.5 sin (3 0^{\circ})

28 sin (4 5^{\circ})

arccos (\frac{8}{12})

(sin (4 5^{\circ}))^{2} + (cos (4 5^{\circ}))^{2}

8 cos (30 0^{\circ})

What is the value of cos(160)cos(40)+sin(160)sin(40) ?
The value of cos(160)cos(40)+sin(160)sin(40) is -1/2