Question

Calculate without resorting to table.
Verify $\cos {20}^{\circ }+2{\sin }^2{55}^{\circ }=1+\sqrt{2}\sin {65}^{\circ }$

Answer 1

$\cos 20°+{2\sin }^{2}55°$

$=\cos 20°-\cos 110°+1$

$=1+\cos 20°-\cos 110°$

$=1+2\sin 60°\sin 45°$

$=1+\sqrt{2}\sin 65°$