Question
Without using trigomentric tables, prove that:
$\sin53^\circ\cos37^\circ+\cos53^\circ\sin37^\circ=1$
$\sin53^\circ\cos37^\circ+\cos53^\circ\sin37^\circ=1$
✓
Answer
$\text{L.H.S}=\sin53^\circ\cos37^\circ+\cos53^\circ\sin37^\circ$
$=\sin\big(90^\circ-37^\circ\big)\cos37^\circ+\cos\big(90^\circ-37^\circ\big)\sin37^\circ$
$=\cos37^\circ\cos37^\circ+\sin37^\circ\sin37^\circ$
$=\cos^237^\circ+\sin^237$
$=1$
$=\text{R.H.S.}$
$=\sin\big(90^\circ-37^\circ\big)\cos37^\circ+\cos\big(90^\circ-37^\circ\big)\sin37^\circ$
$=\cos37^\circ\cos37^\circ+\sin37^\circ\sin37^\circ$
$=\cos^237^\circ+\sin^237$
$=1$
$=\text{R.H.S.}$
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