If sin θ = $\frac{4}{5}$ where 0° ∠ θ ∠ 90º, what is the value of cos θ + tan θ?

Analyze the question: We're given sin θ = 4/5 with θ acute (between 0° and 90°). We need cos θ + tan θ.

Concept: Use a right-angled triangle, where sin θ = opposite/hypotenuse. Then find the adjacent side with Pythagoras' theorem.

Solution:

1. Opposite = 4, hypotenuse = 5.
2. Adjacent = √(5² − 4²) = √(25 − 16) = √9 = 3 (the 3-4-5 triple).
3. cos θ = adjacent/hypotenuse = 3/5.
4. tan θ = opposite/adjacent = 4/3.

Now add them:

cos θ + tan θ = 3/5 + 4/3

The LCM of 5 and 3 is 15:

= 9/15 + 20/15 = 29/15

Answer: The value is 29/15, which matches option B.

Tip: Memorise the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17). They save time in trigonometry questions. Also, since θ is acute, all the ratios are positive, so you don't need to worry about signs.