​ 1. Convert 2 π/3 radian measure into degree measure. ​

Question

1. Convert \(\frac{2 \pi}{3}\) radian measure into degree measure.

2. Prove that \(\frac{sin\, 5x + sin\, 3x}{cos\, 5x + cos \,3x}\) = tan 4x

Answer 1

1. \(\frac{2 \pi}{3}\) = \(\frac{2 \pi}{3}\) x \(\frac{180}{\pi}\) = 120°

2. LHS

\(\frac{sin\, 5x + sin\, 3x}{cos\, 5x + cos \,3x}\)

= \(\frac{2sin 4x \,cos x}{2 cos 4x \,cos x}\)

= \(\frac{sin\, 4x}{cos \, 4x}\)

= tan 4x