Question
Without using trigomentric tables, prove that:
$\sin35^\circ\sin55^\circ+\cos35^\circ\cos55^\circ=0$
$\sin35^\circ\sin55^\circ+\cos35^\circ\cos55^\circ=0$
✓
Answer
$\text{L.H.S}=\sin35^\circ\sin55^\circ+\cos35^\circ\cos55^\circ$
$=\sin35^\circ\cos\big(90^\circ-55^\circ\big)-\cos35^\circ\sin\big(90^\circ-55^\circ\big)$
$=\sin35^\circ\cos35^\circ-\cos35^\circ\sin35^\circ$
$=0$
$=\text{R.H.S.}$
$=\sin35^\circ\cos\big(90^\circ-55^\circ\big)-\cos35^\circ\sin\big(90^\circ-55^\circ\big)$
$=\sin35^\circ\cos35^\circ-\cos35^\circ\sin35^\circ$
$=0$
$=\text{R.H.S.}$
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