Simplify ${cos 60}^{\circ} {cos 30}^{\circ} + {sin 60}^{\circ} {sin 30}^{\circ}$ $cos60^@cos30^@+sin60^@sin30^@$ ?

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Answer 1 · 2017-03-23T16:38:44

${cos 60}^{\circ} {cos 30}^{\circ} + {sin 60}^{\circ} {sin 30}^{\circ} = \frac{\sqrt{3}}{2}$ $cos60^@cos30^@+sin60^@sin30^@=sqrt3/2$

Here we use the identity $cos A cos B + sin A sin B = cos (A - B)$ $cosAcosB+sinAsinB=cos(A-B)$

As we have $A = 60^{\circ}$ $A=60^@$ and $B = 30^{\circ}$ $B=30^@$

${cos 60}^{\circ} {cos 30}^{\circ} + {sin 60}^{\circ} {sin 30}^{\circ}$ $cos60^@cos30^@+sin60^@sin30^@$

= $cos (60^{\circ} - 30^{\circ})$ $cos(60^@-30^@)$

= ${cos 30}^{\circ}$ $cos30^@$

= $\frac{\sqrt{3}}{2}$ $sqrt3/2$

Simplify cos60∘cos30∘+sin60∘sin30∘cos60^@cos30^@+sin60^@sin30^@?