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Question

If x=cosec2θ,y=sec2θ,z=11sin2θcos2θ then tan3θtanθ is equal to

A
(3x4)y(43y)x
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B
(43y)x(3x4)y
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C
(43x)y(43y)x
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D
(y/3)3/2
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Solution

The correct option is A (3x4)y(43y)x
Given x=cosec2θ,y=sec2θ,z=11sin2θcos2θ

sin2θ=1x,cos2θ=1y,1sin2θcos2θ=1z

tan3θ=sin3θcos3θ=3sinθ4sin3θ4cos3θ3cosθ=tanθ(34sin2θ4cos2θ3)

tan3θtanθ=34x4y3=(3x4)y(43y)x

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