What is the value of -4cos((7pi)/(12))cos((5pi)/(12)) ?

The value of -4cos((7pi)/(12))cos((5pi)/(12)) is 2-sqrt(3)

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-4cos((7pi)/(12))cos((5pi)/(12))

- 4 cos (\frac{7 π}{12}) cos (\frac{5 π}{12})

2 - 3

Solution steps

- 4 cos (\frac{7 π}{12}) cos (\frac{5 π}{12})

Rewrite using trig identities:

4 cos (\frac{7 π}{12}) cos (\frac{5 π}{12}) = 2 (cos (π) + cos (\frac{π}{6}))

= - 2 (cos (π) + cos (\frac{π}{6}))

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

= - 2 (- 1 + \frac{3}{2})

Simplify

- 2 (- 1 + \frac{3}{2}) : 2 - 3

= 2 - 3

sec (1.24)

cos (16 2^{\circ})

arctan (\frac{- 3}{1})

arccos (15)

cos^{2} (1 5^{\circ}) + sin^{2} (1 5^{\circ})

What is the value of -4cos((7pi)/(12))cos((5pi)/(12)) ?
The value of -4cos((7pi)/(12))cos((5pi)/(12)) is 2-sqrt(3)