Question #23b80

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Answer 1 · 2018-01-26T12:53:10

# theta= 60^o or theta= 300^o#

#2cos^2θ−3sinθ=0#

#2(1-sin^2theta)−3sinθ=0# because # cos^2θ+sin^2theta=1#

#2-2sin^2theta−3sinθ=0#

#2sin^2theta+3sinθ-2=0#

#sinθ=(-3+-sqrt(3^2-4*2*(-2)))/(2*2)#

#sinθ=(-3+-sqrt(9+16))/4#

#sinθ=(-3+-sqrt(25))/4=(-3+-5)/4#

#sin theta=-8/4 or sin theta= 2/4#

#sin theta=-2 or sin theta= 1/2#

# theta notin RR or sin theta= 1/2#

# theta= 60^o or theta= (-60^o +360^o)#

# theta= 60^o or theta= 300^o#