How do you solve for x in cos(-100)= cos(55)cos x+sin(55)sin xcos(100)=cos(55)cosx+sin(55)sinx?

2 Answers
Jul 21, 2018

x in {360k+155}uu{360k-45}, k in ZZ.

Explanation:

Given eqn. is, cos55cosx+sin55sinx=cos(-100).

:. cos(x-55)=cos100.

But, costheta=cosalpha rArr theta=2kpi+-alpha, k in ZZ.

:. cos(x-55)=cos100 rArr x-55=360k+-100, k in ZZ.

:. x=360k+55+-100, k in ZZ.

:. x in {360k+155}uu{360k-45}, k in ZZ.

x=55+2n\pi\pm 100

Where, n is any integer

Explanation:

Given trigonometric equation:

\cos(-100)=\cos(55)\cosx+\sin(55)\sin x

\cos(100)=\cos(55-x)

\cos(55-x)=\cos(100)

\cos(x-55)=\cos(100)

x-55=2n\pi\pm 100

x=55+2n\pi\pm 100

Where, n is any integer i.e. n=0, \pm1, \pm2, \pm3, \ldots