Question

If tan $\theta$, 2 tan $\theta$ + 2, 3 tan $\theta$ + 3 are in G.P. then the value of $\frac{7-5cot\theta }{9-4\sqrt{se{c}^2\theta -1}}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$(2tan\theta +2{)}^2=tan\theta (3tan\theta +3)\Rightarrow ta{n}^2\theta +5tan\theta +4=0\Rightarrow tan\theta =-1,-4$ but tan $\theta$ = – 4 is only satisfies above condition