Question

Cos a=1/7 , cos b=13/14 a,b acute angle show that a-b =60

Answer 1

$\cos a = \frac{1}{7} \\ \sin a = \sqrt{1 - {( \frac{1}{7}) }^{2} } = \frac{4 \sqrt{3} }{7} \\ \cos b = \frac{13}{14} \\ \sin b = \sqrt{1 - {( \frac{13}{14}) }^{2} } = \frac{3\sqrt{3} }{14} \\ \\ \cos (a - b) = \cos a\cos b + \sin a\sin b \\ = \frac{1}{7} \times \frac{13}{14} + \frac{4 \sqrt{3} }{7} \times \frac{3 \sqrt{3} }{14} \\ = \frac{49}{7 \times 14} = \frac{1}{2} \\ so \: \: a - b = 60 \: degree$