Question

How do you solve for x in $cos(-100)=cos\left(55\right)cosx+sin\left(55\right)sinx?$

Answer 1

Given trigonometric equation :

$cos(-100)=cos\left(55\right)cosx+sin\left(55\right)sinx$

$cos\left(100\right)=cos(55-x)$

$cos(55-x)=cos\left(100\right)$

$cos(x-55)=cos\left(100\right)$

$x-55=2n\pi \pm 100$

$x=55+2n\pi \pm 100$

Where n is any integer i.e. $n=0,\pm 1,\pm 2,\pm 3$....