If cotθ = √7, then the value of cose c^2 - ^2 cose c^2 + ^2 is:

Answer: Option A

$$\begin{array}{rl}& \cot \theta =\sqrt{7}\\ & \frac{\text{cose}{\text{c}}^2\theta -{\sec }^2\theta }{\text{cose}{\text{c}}^2\theta +{\sec }^2\theta }\\ & =\frac{{\cos }^2\theta -{\sin }^2\theta }{{\cos }^2\theta +{\sin }^2\theta }\\ & \text{Divide by }{\sin }^2\theta \\ & =\frac{\frac{{\cos }^2\theta }{{\sin }^2\theta }-\frac{{\sin }^2\theta }{{\sin }^2\theta }}{\frac{{\cos }^2\theta }{{\sin }^2\theta }+\frac{{\sin }^2\theta }{{\sin }^2\theta }}\\ & =\frac{{\cot }^2\theta -1}{{\cot }^2\theta +1}\\ & =\frac{7-1}{7+1}\\ & =\frac{6}{8}\\ & =\frac{3}{4}\end{array}$$