Explanation

The recovered question (testbook question bank, options matching exactly) is: if cot(theta)=sqrt(7), find (cosec^2(theta)-sec^2(theta))/(cosec^2(theta)+sec^2(theta)). Since tan^2(theta)=1/7, dividing top and bottom by sin^2(theta) gives (1-tan^2(theta))/(1+tan^2(theta))=(1-1/7)/(1+1/7)=(6/7)/(8/7)=3/4. The stored key B (1/3) was wrong; the corrected answer is D (3/4), agreeing with the published coaching key.