The expression that is equal to sin 72° is sin(90° – 18°), which can also be expressed as cos(18°). This is derived from the co-function identity of sine and cosine.
To understand this, we can use the complementary angle property of trigonometric functions. According to this property, the sine of an angle is equal to the cosine of its complement. In this case, since 90° – 72° = 18°, we can say:
sin(72°) = cos(18°)
Furthermore, if you have access to a calculator or a trigonometric table, you can find the exact values for these angles and verify that they produce the same result. This is particularly useful in solving problems that involve finding the values of trigonometric functions without using a calculator directly.