Final answer:
The trigonometric expression (sin30° + cos60°) cot30° simplifies to √3 by using known values sin30° and cos60° (both equal to ½) and cot30° (equal to √3).
Step-by-step explanation:
The subject of the problem given is related to trigonometry, which is a branch of mathematics that studies the relationships between the angles and sides of triangles.
The original question asks to evaluate the trigonometric expression (sin30° + cos60°) cot30°.
Before we begin solving, it's important to note that the Law of Sines and the Law of Cosines are fundamental in solving various problems involving triangles.
However, in this particular problem, we are dealing with trigonometric identities and the known values of trigonometric functions at specific angles to simplify the expression.
Solving the problem:
- sin30° is equal to ½.
- cos60° is also equal to ½.
- cot30° is the reciprocal of tan30°, which is √3.
- Now, we add sin30° and cos60°: ½ + ½ = 1.
- Multiplying this by cot30°: 1 × √3 = √3.
Hence, the simplified result of the expression (sin30° + cos60°) cot30° is √3.