Question #d974d

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Answer 1 · 2017-07-18T06:56:47

The solutions are #S={133.11^@, 226.89^@}#

We solve this equation like a quadratic equation

#ax^2+bx+c=0#

#cos^2theta+8costheta+5=0#

The discriminant is

#Delta=b^2-4ac#

#Delta=8^2-4*1*5=64-20=44#

As, #Delta>0#, there are 2 real solutions

#costheta=(-b+-sqrtDelta)/(2a)#

#=(-8+-sqrt44)/(2)=-4+-sqrt11#

So,

#costheta=-4-sqrt11=-7.3#

This is not possible as #-1<=costheta<=1#

#costheta=sqrt11-4=-0.6834#

#theta=133.11^@# or #theta=226.89^@#

#theta=2.32+2pin# and #theta=-2.32+2pin#, #n in ZZ#