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

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Answer 1 · 2018-07-21T15:06:41

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

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#.

Answer 2 · 2018-07-21T17:15:02

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

Where, #n# is any integer

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#