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

The solution to 2cos(1/2 x-3)-1 is 2cos(3-x/2)-1

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

simplify

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

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

Solution steps

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

Rewrite using trig identities

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

Use the Angle Difference identity:

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

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

tan (arcsec (\frac{x}{2}))

tan (arccos (\frac{y}{8}))

cos (a - 3 0^{\circ})

cos (arctan (\frac{a}{b}))

2 sin (x - \frac{π}{3})