Simplify the trigonometric expression: (sin(x) / (1 + cos(x))) + ((1 + cos(x)) / sin(x)).
Answer and explanation
Correct answer: B. 2 csc(x)
- Step 1: Common denominator: (sin^2(x) + (1 + cos(x))^2) / (sin(x)(1 + cos(x))). Step 2. Numerator: sin^2(x) + 1 + 2cos(x) + cos^2(x) = 2 + 2cos(x) = 2(1 + cos(x)). Step 3. Divide: 2(1 + cos(x)) / (sin(x)(1 + cos(x))) = 2 / sin(x) = 2 csc(x). Answer: 2 csc(x). Why not the others: 2 sec(x) is 2 / cos(x).
Practise more Euclidean Geometry and Trigonometry.
Free questions with an explanation for every one, and full timed University of the Philippines College Admission Test mock tests.
More Euclidean Geometry and Trigonometry questions
- The interior angles of a triangle are in the ratio 2 : 3 : 5. What is the measure of the largest angle?
- A right triangle has legs of lengths 9 cm and 12 cm. What is the length of its hypotenuse?
- What is the area of a circular sector with radius 6 cm and central angle 60 degrees?
- An inscribed angle in a circle intercepts an arc measuring 110 degrees. What is the measure of the inscribed angle?
- Two similar triangles have corresponding sides in the ratio 3 : 5. If the area of the smaller triangle is 36 cm^2, what is the area of the l…
- What is the distance between the points (-2, 5) and (4, -3) in the Cartesian plane?