Find the value of sin 45° - cos 30°

  • A \(\frac{2+\sqrt{3}}{4}\)
  • B \(\frac{\sqrt{2}+\sqrt{3}}{4}\)
  • C \(\frac{\sqrt{2}+\sqrt{3}}{2}\)
  • D \(\frac{\sqrt{2}-\sqrt{3}}{2}\)
jamb 2009mathematics

The correct answer is D. \(\frac{\sqrt{2}-\sqrt{3}}{2}\)

The value of sin 45° - cos 30° can be calculated using the exact values of the trigonometric functions for these angles. The exact value of sin 45° is √2/2, and the exact value of cos 30° is √3/2. Substituting these values into the expression, we get:

sin 45° - cos 30° = √2/2 - √3/2

= (√2 - √3)/2

So, the value of sin 45° - cos 30° is (√2 - √3)/2.

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