Final answer:
The trigonometric identity cos(x°)=sin(90−x°) is true for an infinite number of x values due to the properties of complementary angles and the periodic nature of the sine and cosine functions.
Step-by-step explanation:
The trigonometric equation cos(x°)=sin(90−x°) is considered a trigonometric identity because it holds true for any angle x. This is due to a fundamental property of complementary angles in right triangles (a. The sum of complementary angles is always 90 degrees). In any right triangle, the cosine of an angle is defined as the adjacent side over the hypotenuse, and the sine of an angle is the opposite side over the hypotenuse. When two angles are complementary, their sine and cosine values are essentially 'flipped'. This is because the side that is adjacent to one angle is opposite to its complementary angle and vice versa.
The reason this identity is true for an infinite number of x values is because c. The sine function is periodic, repeating every 360 degrees, and similarly for the cosine function. This periodic nature allows the identity to persist through all rotations of the circle, proving true for every possible angle x. Moreover, the identity is part of a series of trigonometric properties that relate the functions of complementary angles, echoing d. The tangent of any angle is equal to the cotangent of its complement.