What is 4sec(x-pi/3) ?

The solution to 4sec(x-pi/3) is 4/(1/2 cos(x)+(sqrt(3))/2 sin(x))

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simplify 4sec(x-pi/3)

simplify

4 sec (x - \frac{π}{3})

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

Solution steps

4 sec (x - \frac{π}{3})

Rewrite using trig identities

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

Simplify

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

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

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What is 4sec(x-pi/3) ?
The solution to 4sec(x-pi/3) is 4/(1/2 cos(x)+(sqrt(3))/2 sin(x))