Question

Evaluate the expression

sin(60∘)+tan(30∘)/cos(60∘)

A)1.732​

B)3.4641​

C)1.7321​

D)0.8660

Answer 1

The expression sin(60°)+tan(30°)/cos(60°) simplifies to √3/2, which is approximately 0.8660, making the correct choice D)0.8660.

Step-by-step explanation:

The question asks us to evaluate the expression sin(60°)+tan(30°)/cos(60°). To do this, let's first recall the values of sine, cosine, and tangent for the angles 30°, 60°, and 45°:

• sin(30°) = 1/2
• sin(60°) = √3/2
• cos(30°) = √3/2
• cos(60°) = 1/2
• tan(30°) = 1/√3

Now we can substitute these values into the expression:

sin(60°) + tan(30°)/cos(60°) = (√3/2) + (1/√3)/(1/2)

We can simplify the second term:

(1/√3)/(1/2) = 2/√3 = 2√3/3

Now add this to sin(60°):

(√3/2) + (2√3/3) = (3√3 + 4√3) / 6 = √3/2

So, the correct answer to the expression is √3/2, which approximates to 0.8660. Thus, the correct choice is D)0.8660.