Question

Evaluate each of the following:
cos60° cos45° - sin60° sin 45°

Answer 1

Answer:

$(1 - \sqrt{3} ) \div 2 \sqrt{3}$

Answer 2

cos60° cos45° - sin60° sin 45° = = √2-√6 / 4

Step-by-step explanation:

Evaluate cos60° cos45° - sin60° sin 45°.

sin 45° = 1/√2

cos 45° = 1/√2

sin 60° = √3/2

cos 60° = 1/2

So cos60° cos45° - sin60° sin 45° = (1/2 * 1/√2) - (√3/2 * 1/√2)

 = 1/2√2 - √3/2√2

 = 1-√3 / 2√2

 = √2 (1-√3) / 4

 = √2-√6 / 4

Value of cos60° cos45° - sin60° sin 45° = = √2-√6 / 4