What is 2tan(-pi/8 b+4) ?

The solution to 2tan(-pi/8 b+4) is 2tan(4-(pib)/8)

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simplify 2tan(-pi/8 b+4)

simplify

2 tan (- \frac{π}{8} b + 4)

2 tan (4 - \frac{πb}{8})

Solution steps

2 tan (- \frac{π}{8} b + 4)

Rewrite using trig identities

= 2 \cdot \frac{sin ( 4 ) cos ( \frac{πb}{8} ) - cos ( 4 ) sin ( \frac{πb}{8} )}{cos ( 4 ) cos ( \frac{πb}{8} ) + sin ( 4 ) sin ( \frac{πb}{8} )}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( sin ( 4 ) cos ( \frac{πb}{8} ) - cos ( 4 ) sin ( \frac{πb}{8} ) ) \cdot 2}{cos ( 4 ) cos ( \frac{πb}{8} ) + sin ( 4 ) sin ( \frac{πb}{8} )}

Use the Angle Difference identity:

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

= \frac{2 sin ( 4 - \frac{πb}{8} )}{cos ( 4 ) cos ( \frac{πb}{8} ) + sin ( 4 ) sin ( \frac{πb}{8} )}

Simplify

cos (4) cos (\frac{πb}{8}) + sin (4) sin (\frac{πb}{8}) : cos (- \frac{πb}{8} + 4)

= \frac{2 sin ( - \frac{πb}{8} + 4 )}{cos ( 4 - \frac{πb}{8} )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= 2 tan (4 - \frac{πb}{8})

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