What is cos(pi/4+P) ?

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

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simplify cos(pi/4+P)

simplify

cos (\frac{π}{4} + P)

- sin (- \frac{π}{4} + P)

Solution steps

cos (\frac{π}{4} + P)

Rewrite using trig identities

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

Rewrite using trig identities

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

Factor

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

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

Express with sin, cos

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

Rewrite using trig identities

= - sin (- \frac{π}{4} + P)

3 sin (2 x - \frac{π}{6})

cos (- 4 r)

tan (π - β) + tan (π + β)

- cot (- x)

csc (x - \frac{3 π}{2})