1

Problem

Evaluate the following expression: \$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$.

2

Step

Let’s evaluate the given expression step by step:

\$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$

3

Step

First, let’s use the trigonometric identities:

\$ sin(pi/3) = \sqrt3 / 2 \$

\$ cos(pi/3) = 1/2 \$

\$ sin(pi/6) = 1/2 \$

\$ cos(pi/6) = \sqrt3 / 2 \$

4

Hint

Now substitute these values into the expression:

\$ \sqrt3 / 2 \times \sqrt3 / 2 + 1/2 \times 1/2 \$

5

Step

Simplify further:

\$ 3/4 + 1/4 \$

6

Step

Combine the terms:

\$ 4/4 = 1 \$

7

Solution

So, the evaluated value of the expression is 1.

8

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

9

Choice-A

This is correct because the result equals 1 after evaluation

Correct 1

10

Choice-B

This is incorrect because after the evaluation the result is not 1

Wrong \$ 1/2\$

11

Choice-C

The evaluation yields a result other than 1, making this statement incorrect

Wrong \$ \sqrt3/2\$

12

Choice-D

The evaluation yields a result other than 1, thus rendering this statement incorrect

Wrong \$ \sqrt 3\$

13

Answer

Option

A

14

Sumup

Please summarize choices