Question

Evaluate cos 30 cos 45 -sin 30 sin 45.

Answer 1

cos 30 cos 45 -sin 30 sin 45

[cos30=√3/2, sin30=1/2,cos45=sin45sin45=1/√2]

Putting in the equation

1(√3-1)/2√2

Hence the value of this equation is (√3-1)/2√2

Answer 2

We need to recall the following trigonometric ratios.

• $cos30^{\textdegree}=\frac{\sqrt{3} }{2}$
• $cos45^{\textdegree} =sin45^{\textdegree}=\frac{1}{\sqrt{2} }$
• $sin30^{\textdegree}=\frac{1}{2}$

This problem is about trigonometric ratios.

Given:

$cos30^{\textdegree} cos45^{\textdegree} -sin30^{\textdegree} sin45^{\textdegree}$

$=\frac{\sqrt{3} }{2}*\frac{1}{\sqrt{2} } -\frac{1}{2} *\frac{1}{\sqrt{2} }$

$=\frac{\sqrt{3} }{2\sqrt{2} }-\frac{1}{2\sqrt{2} }$

$=\frac{\sqrt{3}-1 }{2\sqrt{2} }$