What is cos(θ+pi/4) ?

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

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simplify cos(θ+pi/4)

simplify

cos (θ + \frac{π}{4})

- sin (- \frac{π}{4} + θ)

Solution steps

cos (θ + \frac{π}{4})

Rewrite using trig identities

= \frac{2 cos ( θ ) - 2 sin ( θ )}{2}

Rewrite using trig identities

= \frac{1 - tan ( θ )}{sec ( θ ) 2}

Factor

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

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

Express with sin, cos

= - \frac{- cos ( θ ) + sin ( θ )}{2}

Rewrite using trig identities

= - sin (- \frac{π}{4} + θ)

tan (arccot (x))

cos (27 0^{\circ} + θ)

sin (arcsec (\frac{x}{8}))

cos (- x) + tan (- x) sin (- x)

- cos (x - \frac{π}{4})