Question
If A = 30° and B = 60°, verify that.
$\cos(\text{A}+\text{B})=\cos\text{A}\cos\text{B}-\sin\text{A}\sin\text{B}$
$\cos(\text{A}+\text{B})=\cos\text{A}\cos\text{B}-\sin\text{A}\sin\text{B}$
✓
Answer
$\cos(\text{A}+\text{B})=\cos\text{A}\cos\text{B}-\sin\text{A}\sin\text{B}$
$\text{A}=30^\circ\ \text{B}=60^\circ$
$\cos(90^\circ)=\cos30^\circ\cos60^\circ-\sin30^\circ\sin60^\circ$
$=\cos(90^\circ)=\frac{1}{2}\cdot\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}\cdot\frac{1}{2}$
$0=0$
$\text{L.H.S} = \text{R.H.S}$
$\text{A}=30^\circ\ \text{B}=60^\circ$
$\cos(90^\circ)=\cos30^\circ\cos60^\circ-\sin30^\circ\sin60^\circ$
$=\cos(90^\circ)=\frac{1}{2}\cdot\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2}\cdot\frac{1}{2}$
$0=0$
$\text{L.H.S} = \text{R.H.S}$
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