What is cos(b-pi/4)-cos(b) ?

The solution to cos(b-pi/4)-cos(b) is (sqrt(2)(cos(b)+sin(b)-sqrt(2)cos(b)))/2

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simplify cos(b-pi/4)-cos(b)

simplify

cos (b - \frac{π}{4}) - cos (b)

\frac{2 ( cos ( b ) + sin ( b ) - 2 cos ( b ) )}{2}

Solution steps

cos (b - \frac{π}{4}) - cos (b)

Rewrite using trig identities

= \frac{2 cos ( b ) + 2 sin ( b )}{2} - cos (b)

Simplify

\frac{2 cos ( b ) + 2 sin ( b )}{2} - cos (b) : \frac{2 ( cos ( b ) + sin ( b ) - 2 cos ( b ) )}{2}

= \frac{2 ( cos ( b ) + sin ( b ) - 2 cos ( b ) )}{2}

\frac{a}{sin ( 6 2 ^{\circ} )}

- cos (2 πn)

tan (arcsin (\frac{1}{2} x))

\frac{1}{sin ( x )} (2 π)

cos (- c + \frac{π}{2})

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