Final answer:
Equations B (cos(75) = sin(15)) and D (cos(15) = sin(75)) are true due to the complementary angle identity in trigonometry. The other equations are not true as they do not satisfy the necessary trigonometric relationships.
Step-by-step explanation:
To determine which of the given equations are true, we can use the properties of trigonometric functions and their relationships. For example, the complementary angle identity states that the sine of an angle is the same as the cosine of its complementary angle. Let's evaluate each statement:
- A. cos(15) ≠ sin(15) because the sine and cosine of the same angle are not equal; this is true only for 45°.
- B. cos(75) = sin(15) because 75° and 15° are complementary angles (75° + 15° = 90°), making this equation true.
- C. cos(75) ≠ cos(15) because these are not complementary angles nor the same angle.
- D. cos(15) = sin(75) because 15° and 75° are complementary (15° + 75° = 90°), making this equation true.
- E. tan(15) ≠ tan(75) because the tangent of non-complementary angles are not equal, and these angles do not satisfy the identity tan(a) = cot(90° - a).
Based on the evaluation, the true equations from the given options are B and D.