What is the value of cos(165)cos(45)+sin(165)sin(45) ?

The value of cos(165)cos(45)+sin(165)sin(45) is -1/2

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cos(165)cos(45)+sin(165)sin(45)

cos (16 5^{\circ}) cos (4 5^{\circ}) + sin (16 5^{\circ}) sin (4 5^{\circ})

- \frac{1}{2}

Solution steps

cos (16 5^{\circ}) cos (4 5^{\circ}) + sin (16 5^{\circ}) sin (4 5^{\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}

\frac{7}{tan ( 4 5 ^{\circ} )}

arcsin (1) - arcsin (- 1)

(sin (1))^{2}

15 csc (2 4^{\circ})

4 sin (25 0^{\circ})

What is the value of cos(165)cos(45)+sin(165)sin(45) ?
The value of cos(165)cos(45)+sin(165)sin(45) is -1/2