Without using trigonometric tables, show that (cos 70°)/(sin 20°) + cos 49° sin41° = 2

Question

Without using trigonometric tables, show that \(\frac{cos\,70°}{sin\,20°}\)+ cos 49° sin 41° = 2

Answer 1

  \(\frac{cos\,70°}{sin\,20°}\)+ cos 49°cosec 41° = \(\frac{cos(90°-20°)}{sin\,20°}+\)cos(90° - 41°)cosec 41°

= \(\frac{sin\,20°}{sin\,20°}+\) sin 41° x \(\frac1{sin\,41°}\) = 1 + 1 = 2.