If tan A + sec A = 3/2 and A is an acute angle, then the value of (10 cot A + 13 cos A) / (12 tan A + 5 cosec A) is:
A.2✓ Correct
B.4
C.5
D.1
Explanation
From tan A + sec A = 3/2, we can solve to find sin A = 5/13 and cos A = 12/13. Substituting: numerator = 10(12/5) + 13(12/13) = 24 + 12 = 36; denominator = 12(5/12) + 5(13/5) = 5 + 13 = 18. Value = 36/18 = 2.
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