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Given that tan(theta) = 1/sqrt(7), evaluate (cosec²(theta) - sec²(theta)) / (cosec²(theta) + sec²(theta)).

1. 3/4
2. 1/2
3. 5/8
4. 2/3

Correct answer: 3/4

Solution

Dividing top and bottom by cosec²(theta) gives (1 - tan²(theta))/(1 + tan²(theta)); with tan²(theta)=1/7 this equals (6/7)/(8/7) = 3/4.

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