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If $\tan θ, 2 \tan θ + 2 and 3 \tan θ + 3$ are in GP, then the value of $\frac{7 - 5 \cot θ}{9 - 4 \sqrt{\sec^{2} θ - 1}}$ is

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Correct option is C

Since, (2tan⁡θ+2)2=tan⁡θ(3tan⁡θ+3)⇒ 4tan2⁡θ+8tan⁡θ+4=3tan2⁡θ+3tan⁡θ⇒ tan2⁡θ+5tan⁡θ+4=0⇒ tan⁡θ+4)(tan⁡θ+1)=0⇒ 7−5cot⁡θ⇒ 7+54=39−4(−4)=33100

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If tan⁡θ,2tan⁡θ+2 and 3tan⁡θ+3 are in GP, then the value of 7−5cot⁡θ9−4sec2⁡θ−1 is

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If $\tan θ, 2 \tan θ + 2 and 3 \tan θ + 3$ are in GP, then the value of $\frac{7 - 5 \cot θ}{9 - 4 \sqrt{\sec^{2} θ - 1}}$ is