Question

Prove that $\frac{sin 70\textdegree - cos 40\textdegree}{cos 50\textdegree - sin 20\textdegree} = \frac{1}{\sqrt{3}}$.

Answer 1

Answer:

$\frac{1}{\sqrt{3}}$

Step-by-step explanation:

Formula used:

$sinC-sinD=2cos(\frac{C+D}{2})sin(\frac{C-D}{2})}$

$\frac{sin70-cos40}{cos50-sin20}$

$=\frac{sin70-sin50}{sin40-sin20}$

$=\frac{2cos(\frac{70+50}{2})sin(\frac{70-50}{2})}{ 2cos(\frac{40+20}{2})sin(\frac{40-20}{2})}$

$=\frac{2cos60\:sin10}{ 2cos30\:sin10}$

$=\frac{cos60}{cos30}$

$=\frac{ \frac{1}{2}}{\frac{\sqrt{3}}{2}}$

$=\frac{1}{\sqrt{3}}$