What is the value of cos((2pi)/3-pi/6) ?

The value of cos((2pi)/3-pi/6) is 0

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cos((2pi)/3-pi/6)

cos (\frac{2 π}{3} - \frac{π}{6})

0

Solution steps

cos (\frac{2 π}{3} - \frac{π}{6})

Rewrite using trig identities:

cos (\frac{2 π}{3}) cos (\frac{π}{6}) + sin (\frac{2 π}{3}) sin (\frac{π}{6})

= cos (\frac{2 π}{3}) cos (\frac{π}{6}) + sin (\frac{2 π}{3}) sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

= 0

sin (2 arccos (- \frac{4}{5}))

tan (2 arcsin (- \frac{4}{5}))

cos (84 0^{\circ})

tan (- \frac{4}{3})

sin^{2} (27 0^{\circ})