To find the value of sin 30° * cot 45° without using a calculator, we can break it down step by step:
1. **sin 30° = 1/2**: The sine of 30 degrees is 1/2. This is a common trigonometric value that can be remembered from the unit circle or by using special triangles.
2. **cot 45° = 1**: The cotangent of 45 degrees is 1. Cotangent is the reciprocal of the tangent function, and for 45 degrees, it equals 1.
Therefore, sin 30° * cot 45° = (1/2) * 1 = 1/2.
Moving on to determine the value of cos 30° * tan 60°:
1. **cos 30° = √3/2**: The cosine of 30 degrees is √3/2. This is another common trigonometric value that can be derived from the unit circle or remembered from special triangles.
2. **tan 60° = √3**: The tangent of 60 degrees is √3. This can be calculated by dividing sin 60° by cos 60°, which equals √3.
Therefore, cos 30° * tan 60° = (√3/2) * √3 = √3/2 * √3 = 3/2.
In conclusion, sin 30° * cot 45° = 1/2 and cos 30° * tan 60° = 3/2.
