2017 · Q50
If A = (sin 45° - sin 30°)/(cos 45° + cos 60°) and B = (sec 45° - tan 45°)/(csc 45° + cot 45°), then which one of the following is correct ?
Elementary MathematicsTrigonometry
- AA = B
- BA > B > 0
- CA < B
- DB < A < 0
Explanation
A = (√2/2−1/2)/(√2/2+1/2) = (√2−1)/(√2+1). B = (√2−1)/(√2+1), since sec 45° = csc 45° = √2 and tan 45° = cot 45° = 1. Thus A = B. Hence option (A).