What is 2cos(x-pi/3)-1 ?

The solution to 2cos(x-pi/3)-1 is cos(x)+sqrt(3)sin(x)-1

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simplify 2cos(x-pi/3)-1

simplify

2 cos (x - \frac{π}{3}) - 1

cos (x) + 3 sin (x) - 1

Solution steps

2 cos (x - \frac{π}{3}) - 1

Rewrite using trig identities

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

Expand

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

= cos (x) + 3 sin (x) - 1

sin (tan (- 1 x))

9 - (3 (sin (θ)))^{2}

\frac{1}{sec ^{2} ( x )} d x

1 - (sin (t))^{2}

(\frac{1 + cos ( 2 θ )}{2}) d θ

What is 2cos(x-pi/3)-1 ?
The solution to 2cos(x-pi/3)-1 is cos(x)+sqrt(3)sin(x)-1