Question

-) If cos A = 1/7 and cos B = 13/14 so prove that cos (A-B) = 1/2​

Answer 1

Answer:

Explanation:

\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