If cot θ = 3/4, 0° < θ < 90°, then find the value of: [(1 + sin θ) / cos θ] + [(1 - sin θ) / cos θ].
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Correct answer: A
Explanation
Given:
cotθ = 3/4, 0° < θ < 90°
By the formula:
cotθ = cosθ / sinθ
[(1 + sinθ) / cosθ] + [(1 − sinθ) / cosθ]
= (1 + sinθ + 1 − sinθ) / cosθ
= 2 / cosθ
cotθ = 3/4
tanθ = 4/3
Let in a right triangle:
opposite side = 4
adjacent side = 3
hypotenuse = 5
cosθ = 3/5
2 / cosθ
= 2 / (3/5)
= 10/3