Question
Without using trignometric tables, prove that:
$\cos81^\circ-\sin9^\circ=0$
$\cos81^\circ-\sin9^\circ=0$
✓
Answer
$\text{L.H.S.}=\cos81^\circ-\sin9^\circ$
$=\cos\big(90^\circ-9^\circ\big)-\sin9^\circ$
$=\sin9^\circ-\sin9^\circ$
$=0$
$=\text{R.H.S}$
$=\cos\big(90^\circ-9^\circ\big)-\sin9^\circ$
$=\sin9^\circ-\sin9^\circ$
$=0$
$=\text{R.H.S}$
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