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Question

If tanθ,2tanθ+2,3tanθ+3 are in G.P., then the value of 75cotθ94sec2θ1 is

A
125
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B
3328
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C
33100
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D
1213
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Solution

The correct option is B 3328

According to the given condition, (2tanθ+2)2=(3tanθ+3)tanθ
4tan2θ+8tanθ+4=3tan2θ+3tanθ
tan2θ+5tanθ+4=0
So, tanθ=1 or 4, but 1 doesn't satisfy the G.P. condition as two terms become 0.
75cotθ94sec2θ1=7+1.25916=8.257=3328


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