Question

Solve:
$2\frac{\tan {57}^o}{\cot {33}^o}-\frac{\cot {70}^o}{\tan {20}^o}-\sqrt{2}\cos {45}^o$

Answer 1

$2\frac{\tan 57°}{\cot 33°}-\frac{\cot 70°}{\tan 20°}-\sqrt{2}\cos 45°$

$=2\frac{\tan (90°-33°)}{\cot 33°}-\frac{\cot 70°}{\tan (90°-70°)}-\sqrt{2}\times \frac{1}{\sqrt{2}}$

$=2\frac{\cot 33°}{\cot 33°}-\frac{\cot 20°}{\cot 20°}-1$

$=2-1-1$

$=0$