What is cos(pi/4+x) ?

The solution to cos(pi/4+x) is -sin(-pi/4+x)

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simplify cos(pi/4+x)

simplify

cos (\frac{π}{4} + x)

- sin (- \frac{π}{4} + x)

Solution steps

cos (\frac{π}{4} + x)

Rewrite using trig identities

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

Rewrite using trig identities

= \frac{1 - tan ( x )}{sec ( x ) 2}

Factor

\frac{1 - tan ( x )}{sec ( x ) 2} : \frac{- 2 ( tan ( x ) - 1 )}{2 sec ( x )}

= \frac{- ( - 1 + tan ( x ) ) 2}{2 sec ( x )}

Express with sin, cos

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

Rewrite using trig identities

= - sin (- \frac{π}{4} + x)

cos (x - \frac{4}{3} π)

cot (2 x - π)

sin (arcsin (\frac{x}{2}))

cos (\frac{π}{2} y - \frac{π}{2})

cos (- 7 t)