What is the value of cos(165)-cos(15) ?

The value of cos(165)-cos(15) is (-sqrt(6)-sqrt(2))/2

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cos(165)-cos(15)

cos (16 5^{\circ}) - cos (1 5^{\circ})

\frac{- 6 - 2}{2}

Solution steps

cos (16 5^{\circ}) - cos (1 5^{\circ})

Rewrite using trig identities:

cos (1 5^{\circ}) = - cos (16 5^{\circ})

= cos (16 5^{\circ}) - (- cos (16 5^{\circ}))

Simplify

= 2 cos (16 5^{\circ})

Rewrite using trig identities:

cos (16 5^{\circ}) = \frac{- 6 - 2}{4}

= 2 \cdot \frac{- 6 - 2}{4}

Simplify

2 \cdot \frac{- 6 - 2}{4} : \frac{- 6 - 2}{2}

= \frac{- 6 - 2}{2}

2 sin (3 0^{\circ}) + 3 cos (6 0^{\circ}) - 3 tan (4 5^{\circ})

cos (arcsin (\frac{4}{5}) + arccos (\frac{3}{5}))

90 sin (6 0^{\circ})

cos (2) (90)

3 tan (4 5^{\circ})

What is the value of cos(165)-cos(15) ?
The value of cos(165)-cos(15) is (-sqrt(6)-sqrt(2))/2