Given that sin x = $\frac{3}{5}$, 0 ≤ x ≤ 90, evaluate (tan x + 2cosx)

Step 1: Analyze the question We're given sin x = 3/5 with x between 0° and 90°, so x is in the first quadrant and all ratios are positive. We need tan x + 2cos x.

Step 2: Concept Use a right-angled triangle: sin x = opposite/hypotenuse. Find the adjacent side with Pythagoras' theorem.

Step 3: Solution

• Opposite = 3, hypotenuse = 5
• Adjacent = √(5² − 3²) = √(25 − 9) = √16 = 4

So:

• cos x = 4/5
• tan x = 3/4

Now evaluate: tan x + 2cos x = 3/4 + 2(4/5) = 3/4 + 8/5

Common denominator 20: = 15/20 + 32/20 = 47/20 = 2 7/20

Step 4: Answer

Tip: Whenever you see 3/5 (or 4/5), think of the 3-4-5 triangle. It appears very often in WASSCE, JAMB and NECO. Also, when converting an improper fraction to a mixed number, divide: 47 ÷ 20 = 2 remainder 7, so 2 7/20.