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Answer 1 · 2017-03-04T02:10:22

#5 cos^2(x)+ 9 sin(x) =9#

#=>5 -5 sin^2(x)+ 9 sin(x) =9#

#=>5 sin^2(x)- 9 sin(x) +9-5=0#

#=>5 sin^2x- 5sinx-4sinx +4=0#

#=>5 sinx(sinx-1)-4(sinx-1)=0#

#=>(sinx-1)(5 sinx-4)=0#

When

#sinx-1=0=>sinx=1=sin(pi/2)#

#=>x=npi+(-1)^npi/2" where " n in ZZ#

Again when

#(5 sinx-4)=0#

# =>sinx =4/5=sin(sin^-1(4/5))#

#=>x=npi+(-1)^nsin^-1(4/5)" where " n in ZZ#

where #sin^-1(4/5)~~0.3pi#