The value of (cos^3 20° - cos^3 70°)/(sin^3 70° - sin^3 20°) is A. 1/2 B. 1/√2 C. 1 D.2

Question

The value of \(\frac{cos^3 20° - cos^3 70°}{sin^3 70° - sin^3 20°}\) is  

A. 1/2 

B. 1/√2 

C. 1 

D.2

Answer 1

\(\frac{cos^3 20° - cos^3 70°}{sin^3 70° - sin^3 20°}\) = \(\frac{cos^3 20° - cos^3 (90°-20°)}{sin^3 (90°-20°) - sin^3 20°}\)

\(\frac{cos^3 20° - sin^3 20°}{cos^3 20° - sin^3 60°}\) = 1