Question: why sin 45 is equal to cos 45?
Answer: Therefore, both the sine and cosine of 45° equal 1/√2 which may also be written √2 / 2. Next consider 30° and 60° angles. In a 30°-60°-90° right triangle, the ratios of the sides are 1 : √3 : 2. It follows that sin 30° = cos 60° = 1/2, and sin 60° = cos 30° = √3 / 2.