Evaluate: sin 30 degrees times cos 60 degrees + cos 30 degrees times sin 60 degrees.

Step 1: Recall standard trigonometric values

To evaluate the expression, we first need to recall the standard trigonometric values for the angles $30^{\circ}$ and $60^{\circ}$. 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.

More from this chapter

• **EXERCISE 8.3** **1.** Express the trigonometric ratios sin A, tan A and sec A in terms of cot A.
• Cos A / 1 + sin a + 1 + sin a / cos A is equal to 2 sec a
• write all the other trigonometric ratios of angle A in terms of sec A
• Express all the trigonometric ratios in terms of Sin A
• Express the trigonometric ratio sign a sec a tan a in terms of cot a
• Prove that √(sec² A + csc² A) = tan A + cot A
• (secθ - tanθ) = (1)/(m) --- (2) Adding (1) & (2) secθ + tanθ + secθ - tanθ = (1)/(m) + (m)/(1) 2secθ = (1 + m²)/(m) secθ = (1 + m²)/(2m) (Hence proved) 2) If as
• If tanθ + secθ = m, prove that secθ = (m² + 1)/(2m).

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