Find the Value of this Expression: sin 30cos 60 + sin 60cos 30

Correct Answer: The value of Sin 30Cos60+Sin 60Cos 30 is equal to 1. 

This question hinges on your understanding of trigonometric functions, specifically sine (sin) and cosine (cos), and their values at specific angles. So, to achieve a value of the given expression, you would have to substitute the values of Sin 30°, Cos 60°, Sin 60°, and Cos 30°

Complete Step-by-Step Answer

Let’s take a look at the following table of trigonometry values to analyse all the options one by one. 

Angle	Sin	Cos	Tan	Cosec	Sec	Cot
0°	0	1	0	–	1	–
30°	1/2	√3/2	1/√3	2	2/√3	√3
45°	√2/2	√2/2	1	√2	√2	1
60°	√3/2	1/2	√3	2/√3	2	1/√3
90°	1	0	–	1	–	0

Step 1: Recall the Trigonometric Values

As you can see in the table above, we have – 

Using standard trigonometric values:

• Sin 30° = 1/2
• Cos 60° = 1/2
• Sin 60° = √3/2
• Cos 30° = √3/2

Step 2: Substitute the Values into the Expression

Now, after the substitution of these trigonometric values in the equation

Sin 30°Cos 60° + Sin 60°Sin 30° you would get,

Then, comes the simplification of this equation, resulting in 

Hence, the value of the expression Sin 30°Cos 60° + Sin 60°Sin 30° = 1

Therefore, option C. 1  would be the correct choice. 

Alternative Solution:

The expression can be rewritten using the Sine Angle Addition Formula:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Here, A = 30° and B = 60°

Substituting into the formula:

sin(30° + 60°) = sin 90°

We know that sin 90° = 1, so the result is 1.

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