What is the value of cos(175)cos(55)+sin(175)sin(55) ?

The value of cos(175)cos(55)+sin(175)sin(55) is -1/2

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cos(175)cos(55)+sin(175)sin(55)

cos (17 5^{\circ}) cos (5 5^{\circ}) + sin (17 5^{\circ}) sin (5 5^{\circ})

- \frac{1}{2}

Solution steps

cos (17 5^{\circ}) cos (5 5^{\circ}) + sin (17 5^{\circ}) sin (5 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}

arcsin (tan (\frac{π}{4}))

csc (2 0^{\circ})

sin (- \frac{8 π}{3})

arccos (0.89)

- 2 cos (\frac{π}{6})

What is the value of cos(175)cos(55)+sin(175)sin(55) ?
The value of cos(175)cos(55)+sin(175)sin(55) is -1/2