simplify cos(45+x)

Solution

simplify

cos (4 5^{\circ} + x)

- sin (- \frac{π}{4} + x)

Solution steps

cos (4 5^{\circ} + 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 (cos (4 5^{\circ} + x))

\frac{d y}{csc ( y )}

90000000 cos (wt) cos (wt + 31.8)

arccos (\frac{1}{cos ( 5 θ )})

cos (t + \frac{3 π}{2}) - 1