simplify cos(45+θ)

Solution

simplify

cos (4 5^{\circ} + θ)

- sin (- \frac{π}{4} + θ)

Solution steps

cos (4 5^{\circ} + θ)

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)

cos (- π t + π)

(sin (t - \frac{π}{6}))^{2}

\frac{tan ( e ) ( x )}{cos ( x )}

s sin^{2} (π - x)

sin (cos^{(- 1)} (x))