Question
Without using trignometric tables, prove that:
$\big(\sin^265^\circ+\cos^225^\circ\big)\big(\sin65^\circ-\cos25^\circ\big)=0$
$\big(\sin^265^\circ+\cos^225^\circ\big)\big(\sin65^\circ-\cos25^\circ\big)=0$
✓
Answer
$\text{L.H.S.}=\big(\sin^265^\circ+\cos^225^\circ\big)\big(\sin65^\circ-\cos25^\circ\big)$
$=\sin^265^\circ-\cos^225^\circ$
$=\sin^2\big(90^\circ-25^\circ\big)-\cos^225^\circ$
$=\cos^225^\circ-\cos25^\circ$
$=0$
$=\text{R.H.S}$
$=\sin^265^\circ-\cos^225^\circ$
$=\sin^2\big(90^\circ-25^\circ\big)-\cos^225^\circ$
$=\cos^225^\circ-\cos25^\circ$
$=0$
$=\text{R.H.S}$
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