What is 4sin(pi/6+x)-cos(x) ?

The solution to 4sin(pi/6+x)-cos(x) is cos(x)+2sqrt(3)sin(x)

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simplify 4sin(pi/6+x)-cos(x)

simplify

4 sin (\frac{π}{6} + x) - cos (x)

cos (x) + 23 sin (x)

Solution steps

4 sin (\frac{π}{6} + x) - cos (x)

Rewrite using trig identities

= 4 (\frac{1}{2} cos (x) + \frac{3}{2} sin (x)) - cos (x)

Simplify

4 (\frac{1}{2} cos (x) + \frac{3}{2} sin (x)) - cos (x) : cos (x) + 23 sin (x)

= cos (x) + 23 sin (x)

- cos (\frac{π}{3} + x)

(4 tan (θ))^{2} + 16

1 + cot^{2} (- θ)

tan^{3} (arcsec (\frac{x}{3}))

tan (arccos (\frac{x}{13}))

What is 4sin(pi/6+x)-cos(x) ?
The solution to 4sin(pi/6+x)-cos(x) is cos(x)+2sqrt(3)sin(x)