Question
If cos A = 4/5 and A is an acute angle, find the value
of 3 tan A + 4 sec A.Solution
Given cos A = 4/5. Using the identity sin² A + cos² A = 1, we find sin A = √(1 - (4/5)²) = √(1 - 16/25) = √(9/25) = 3/5. Now, tan A = sin A / cos A = (3/5) / (4/5) = 3/4, and sec A = 1 / cos A = 5/4. So, 3 tan A + 4 sec A = 3 * (3/4) + 4 * (5/4) = 9/4 + 20/4 = 29/4 = 7.25. Answer: c) 7.25
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