Question
Without using trignometric tables, prove that:
$\sin^248^\circ+\sin^242^\circ=1$
$\sin^248^\circ+\sin^242^\circ=1$
✓
Answer
$\text{L.H.S.}=\sin^248^\circ+\sin^242^\circ$
$=\sin^2\big(90^\circ-42^\circ\big)+\sin^242^\circ$
$=\cos^242^\circ+\sin^242^\circ$
$=1$
$=\text{R.H.S}$
$=\sin^2\big(90^\circ-42^\circ\big)+\sin^242^\circ$
$=\cos^242^\circ+\sin^242^\circ$
$=1$
$=\text{R.H.S}$
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