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Popular >

simplify cos(x+45)

Solution

simplify

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

Solution

- sin (- \frac{π}{4} + x)

Solution steps

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

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)

Popular Examples

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1 + cot^{2} (x)

simplify tan(x-pi/4)simplify

tan (x - \frac{π}{4})

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cos (n (- π))

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sin (x - \frac{3 π}{2})

simplify cos(pi/3+x)simplify

cos (\frac{π}{3} + x)

Frequently Asked Questions (FAQ)

What is cos(x+45) ?
The solution to cos(x+45) is -sin(-pi/4+x)