Question

4. sin157° = sin23° ​

Answer 1

Ответ:

sin157-sin23=2cos(157+23/2)sin(157-23/2)=2cos90×sin67=2×0×sin67=0

Answer 2

The equation you've written, sin(157°) = sin(23°), is not true. In trigonometry, the sine function is not symmetric in the way that this equation suggests.

The sine function is periodic with a period of 360 degrees (or 2π radians), which means that sin(x) = sin(x + 360°) for any angle x. Additionally, sin(x) = sin(180° - x), which gives a symmetry property around the line x = 90°.

In the case of sin(157°) and sin(23°), these angles are not related by the symmetry properties of the sine function, and their sine values are not equal.

sin(157°) is a negative value because it lies in the third quadrant of the unit circle, where the sine function is negative. On the other hand, sin(23°) is a positive value because it lies in the first quadrant, where the sine function is positive.

If you were trying to solve an equation involving these angles, please double-check the equation and the angles involved.