What is cos(x-pi/3)-2cos(x) ?

The solution to cos(x-pi/3)-2cos(x) is -3/2 cos(x)+(sqrt(3))/2 sin(x)

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simplify cos(x-pi/3)-2cos(x)

simplify

cos (x - \frac{π}{3}) - 2 cos (x)

- \frac{3}{2} cos (x) + \frac{3}{2} sin (x)

Solution steps

cos (x - \frac{π}{3}) - 2 cos (x)

Rewrite using trig identities

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

Add similar elements:

\frac{1}{2} cos (x) - 2 cos (x) = - \frac{3}{2} cos (x)

= - \frac{3}{2} cos (x) + \frac{3}{2} sin (x)

cos (\frac{3 π}{2} - x)

- cos (nπ)

sin (x - 9 0^{\circ})

cos (27 0^{\circ} + x)

tan (arccos (\frac{y}{9}))

What is cos(x-pi/3)-2cos(x) ?
The solution to cos(x-pi/3)-2cos(x) is -3/2 cos(x)+(sqrt(3))/2 sin(x)