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Question

If x = a sin θ and y = b tan θ, then prove that a2x2b2y2=1

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Solution

We have ,
L.H.S=a2x2b2y2

L.H.S=a2a2sin2θb2b2tan2θ [x=asinθ,y=btanθ]

L.H.S=1sin2θ1tan2θ

L.H.S=cosec2θcot2θ [1+cot2θ=cosec2θcosec2θcot2θ=1]

LHS =1= RHS

Hence, proved

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