Question

The value of cos 60° cos 30°- sin 60° sin 30° is

• A. \(\frac{1}{2}\)
• B. \(\frac{\sqrt{3}}{2}\)
• C. 0
• D. 1

Answer 1

The Correct Option is C

To solve the problem, we need to evaluate the trigonometric expression:
$ \cos 60^\circ \cos 30^\circ - \sin 60^\circ \sin 30^\circ $

1. Recognizing the Identity:
This expression matches the cosine angle addition identity:

$ \cos(A + B) = \cos A \cos B - \sin A \sin B $

So,
$ \cos 60^\circ \cos 30^\circ - \sin 60^\circ \sin 30^\circ = \cos(60^\circ + 30^\circ) = \cos(90^\circ) $

2. Using Trigonometric Values:
$ \cos(90^\circ) = 0 $

Final Answer:
The value of the expression is $ 0 $.