What is expand-1+6cos((2pi)/7 (x-5)) ?

The solution to expand-1+6cos((2pi)/7 (x-5)) is -1+6cos((10pi-2pix)/7)

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expand-1+6cos((2pi)/7 (x-5))

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- 1 + 6 cos (\frac{2 π}{7} (x - 5))

- 1 + 6 cos (\frac{10 π - 2 π x}{7})

Solution steps

- 1 + 6 cos (\frac{2 π}{7} (x - 5))

6 cos (\frac{2 π}{7} (x - 5)) = 6 (cos (\frac{10 π}{7}) cos (\frac{2 π x}{7}) + sin (\frac{10 π}{7}) sin (\frac{2 π x}{7}))

= - 1 + 6 (cos (\frac{10 π}{7}) cos (\frac{2 π x}{7}) + sin (\frac{10 π}{7}) sin (\frac{2 π x}{7}))

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= - 1 + 6 cos (\frac{10 π}{7} - \frac{2 π x}{7})

Join

\frac{10 π}{7} - \frac{2 π x}{7} : \frac{10 π - 2 π x}{7}

= - 1 + 6 cos (\frac{- 2 π x + 10 π}{7})

(x - 1)^{2} + (y - 2)^{2} - 25 P (5, - 1)

(x - 4) ln (x - 4) - x + 4

\frac{y ( - 2 y + 2 ) ^{3}}{3}

(e^{c o s (x)}) (1 - cos (y))

\frac{1}{( s \cdot ( s + 2 ) )}

What is expand-1+6cos((2pi)/7 (x-5)) ?
The solution to expand-1+6cos((2pi)/7 (x-5)) is -1+6cos((10pi-2pix)/7)