Question #15764

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Answer 1 · 2018-01-27T03:10:25

#5sin^2 x-7sinxcosx+16cos^2 x=4#

#=>5sin^2x-7sinxcosx+16cos^2x-4sin^2x-4cos^2x=0#

#=>sin^2x-7sinxcosx+12cos^2x=0#

#=>sin^2x-4sinxcosx-3sinxcosx+12cos^2x=0#

#=>sinx(sinx-4cosx)-3cosx(sinx-4cosx)=0#

#=>(sinx-4cosx)(sinx-3cosx)=0#

So #sinx-4cosx=0andsinx-3cosx=0#

When

#sinx-4cosx=0#

#=>sinx/cosx=4#

#=>tanx=tan(tan^-1 4)#

#=>x=npi+tan^-1 4" where "ninZZ#

Similarly

When

#sinx-3cosx=0#

#=>sinx/cosx=3#

#=>tanx=tan(tan^-1 3)#

#=>x=kpi+tan^-1 3" where "kinZZ#