Evaluate: sin 30 degrees times cos 60 degrees + cos 30 degrees times sin 60 degrees.
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Step-by-Step Solution
Step 1: Recall standard trigonometric values
To evaluate the expression, we first need to recall the standard trigonometric values for the angles 30∘ and 60∘. These values are fundamental in trigonometry and are often memorized.
Step 2: Substitute the values into the expression
Now, substitute the recalled trigonometric values into the given expression. This replaces the trigonometric functions with their numerical equivalents, preparing the expression for arithmetic calculation.
Step 3: Perform the multiplications
Perform the multiplication operations in each term. Multiply the numerators and denominators separately for each product.
Step 4: Add the fractions
Finally, add the resulting fractions. Since they have a common denominator, simply add the numerators and keep the denominator the same. Simplify the result to get the final answer.