If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
Question 1 Report
If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
Answer Details
We are given that \(\tan x = \frac{3}{4}\) and \(0 < x < 90^o\).
Since \(\tan x = \frac{\sin x}{\cos x}\), we can rewrite the given equation as:
\[\frac{\sin x}{\cos x} = \frac{3}{4}\]
Multiplying both sides by \(\cos x\) gives us:
\[\sin x = \frac{3}{4}\cos x\]
Dividing both sides by \(2\sin x\) gives us:
\[\frac{\cos x}{2\sin x} = \frac{\frac{4}{3}\sin x}{2\sin x} = \frac{4}{3} \cdot \frac{1}{2} = \frac{2}{3}\]
Therefore, the value of \(\frac{\cos x}{2\sin x}\) is \(\frac{2}{3}\).
Hence, the answer is: \(\frac{2}{3}\).
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