What is the value of -cos((4pi)/3)+cos((2pi)/3) ?

The value of -cos((4pi)/3)+cos((2pi)/3) is 0

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-cos((4pi)/3)+cos((2pi)/3)

- cos (\frac{4 π}{3}) + cos (\frac{2 π}{3})

0

Solution steps

- cos (\frac{4 π}{3}) + cos (\frac{2 π}{3})

Rewrite using trig identities:

cos (\frac{4 π}{3}) = 2 cos^{2} (\frac{2 π}{3}) - 1

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

Simplify

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

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

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

Simplify

- 2 (- \frac{1}{2})^{2} + 1 - \frac{1}{2} : 0

= 0

sec^{2} (\frac{7 π}{6})

sin (7 \frac{π}{2})

cos (arcsin (- 0.845))

\frac{tan ( 2 5 ^{\circ} ) + tan ( 2 0 ^{\circ} )}{1 - tan ( 2 5 ^{\circ} ) tan ( 2 0 ^{\circ} )}

sin (9 4^{\circ})

What is the value of -cos((4pi)/3)+cos((2pi)/3) ?
The value of -cos((4pi)/3)+cos((2pi)/3) is 0