Question #92197

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Answer 1 · 2018-02-05T02:08:03

# (2cot(θ)+cosec(θ))^2 -cosec^2(θ) (4cos(θ) +5cos^2(θ)) #

#= (2cos(θ)cosectheta+cosec(θ))^2 -cosec^2(θ) (4cos(θ) +5cos^2(θ)) #

#= cosec^2theta(2cos(θ)+1)^2 -cosec^2(θ) (4cos(θ) +5cos^2(θ)) #

#= cosec^2theta[(2cos(θ)+1)^2 -(4cos(θ) +5cos^2(θ))] #

#= cosec^2theta(4cos^2(θ)+4costheta +1-4cos(θ) -5cos^2(θ)) #

#= cosec^2theta(1 -cos^2(θ)) #

#= cosec^2theta*sin^2(θ) #

#=1#