The value of sin 264° + cos 64° sin 26° + 2 cos 43° cosec 47° is:
3
The expression is \(\sin^2 64^\circ + \cos 64^\circ \sin 26^\circ + 2\cos 43^\circ \csc 47^\circ\).
Step 1 — Simplify the second term using complementary angles:
Since \(\sin 26^\circ = \cos 64^\circ\), we get \(\cos 64^\circ \sin 26^\circ = \cos^2 64^\circ\). So the first two terms become \(\sin^2 64^\circ + \cos^2 64^\circ = 1\).
Step 2 — Simplify the third term:
\(\csc 47^\circ = \sec 43^\circ = \dfrac{1}{\cos 43^\circ}\), so \(2\cos 43^\circ \csc 47^\circ = \dfrac{2\cos 43^\circ}{\cos 43^\circ} = 2\).
Therefore the value is \(1 + 2 = \mathbf{3}\).
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