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Question

The equation sin2θ4sin3θ1=14sin3θ1 has

A
no root
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B
one root
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C
two root
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D
infinite roots
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Solution

The correct option is D infinite roots
sin2θ4sin3θ1=14sin3θ1
= sin2θ=1
= sinθ=±1
But sinθ1
Thus, sinθ=1
θ=3π2,7π2...
hence, the equation has infinite solutions.

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