What is cos(x+pi/4) ?

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

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simplify cos(x+pi/4)

simplify

cos (x + \frac{π}{4})

- sin (- \frac{π}{4} + x)

Solution steps

cos (x + \frac{π}{4})

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)

sin (arctan (\frac{x}{4}))

cos (x + 9 0^{\circ})

cos (x - \frac{π}{4})

cos (π + nπ)

cos (arcsin (3 x))