Question

Use an addition or subtraction formula to write the expression as a trigonometric function of one number. sin(14°) cos(31°) cos(14°) sin(31°)

Answer 1

To write the expression sin(14°) cos(31°) cos(14°) sin(31°) as a trigonometric function of one number, we use the addition formula sin(A + B) = sin(A) cos(B) + cos(A) sin(B). Breaking down the expression step by step, we find that it can be written as sin(45°) cos(17°).

Step-by-step explanation:

To write the expression sin(14°) cos(31°) cos(14°) sin(31°) as a trigonometric function of one number using an addition or subtraction formula, we can use the formula sin(A + B) = sin(A) cos(B) + cos(A) sin(B). Let's break down the expression step by step:

1. sin(14°) cos(31°) cos(14°) sin(31°)
2. Using the addition formula, we can rewrite this as: sin(14° + 31°) cos(14° - 31°)
3. Combining the angles, we get sin(45°) cos(-17°)
4. Since cos(-17°) is equal to cos(17°), the final expression is sin(45°) cos(17°)

Therefore, the expression sin(14°) cos(31°) cos(14°) sin(31°) can be written as the trigonometric function sin(45°) cos(17°).