Question

Exact value of $\cos {20}^o+2{\sin }^2{55}^o-\sqrt{2}\sin {65}^o$ is

• A. $1$
• B. $\frac{1}{\sqrt{2}}$
• C. $\sqrt{2}$
• D. zero

Answer 1

Answer: (A)

$1$

$\cos {20}^0+2{\sin }^2{55}^0-\sqrt{2}\sin {65}^0$
$=\cos {20}^0+1-\cos {110}^0-\sqrt{2}\sin {65}^0$
$=\cos {20}^0-\cos {110}^0+1-\sqrt{2}\sin {65}^0$
$=2\sin \left({45}^0\right)\left(\sin \right({65}^0\left)\right)-\sqrt{2}\sin {65}^0+1$
$=\sin {65}^0[2\sin {45}^0-\sqrt{2}]+1$
$=0+1$
$=1$