What is expand-6cos(pi/(20)(x+pi))+53dx ?

The solution to expand-6cos(pi/(20)(x+pi))+53dx is -6cos((pi^2+pix)/(20))+53dx

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expand-6cos(pi/(20)(x+pi))+53dx

expand

- 6 cos (\frac{π}{20} (x + π)) + 53 d x

- 6 cos (\frac{π ^{2} + π x}{20}) + 53 d x

Solution steps

- 6 cos (\frac{π}{20} (x + π)) + 53 d x

6 cos (\frac{π}{20} (x + π)) = 6 (cos (\frac{π ^{2}}{20}) cos (\frac{π x}{20}) - sin (\frac{π ^{2}}{20}) sin (\frac{π x}{20}))

= - 6 (cos (\frac{π ^{2}}{20}) cos (\frac{π x}{20}) - sin (\frac{π ^{2}}{20}) sin (\frac{π x}{20})) + 53 d x

Use the Angle Sum identity:

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

= - 6 cos (\frac{π ^{2}}{20} + \frac{π x}{20}) + 53 d x

Join

\frac{π ^{2}}{20} + \frac{π x}{20} : \frac{π ^{2} + π x}{20}

= - 6 cos (\frac{π x + π ^{2}}{20}) + 53 d x

(1 - \frac{1}{n}) (2 - \frac{1}{n})

(2 u^{2} + 2 v^{2}) 2 u^{2} + 2 v^{2} + 4

(3 - 1 - 4 x) (3 + 1 - 4 x)

(4 + sin (θ))^{2}

lo g_{10} (3 \frac{x}{z})

What is expand-6cos(pi/(20)(x+pi))+53dx ?
The solution to expand-6cos(pi/(20)(x+pi))+53dx is -6cos((pi^2+pix)/(20))+53dx