bemath-Given-2cos-x-7cos-y-5-2sin-x-7sin-y-6-cos-x-y-

Question Number 106950 by bemath last updated on 08/Aug/20

^{@ b e m a t h @}

G i v e n {\begin{cases} 2 \cos x + 7 \cos y = 5 \\ 2 \sin x + 7 \sin y = 6 \end{cases}

\cos (x - y) = ?

Answered by john santu last updated on 08/Aug/20

⧫ JS ◊

\to {\begin{cases} 4 \cos^{2} x + 14 \cos xcos y + 49 \cos^{2} y = 25 \\ 4 \sin^{2} x + 14 \sin xsin y + 49 \sin^{2} y = 36 \end{cases}

(1) + (2) \Rightarrow 53 + 14 \cos (x - y) = 61

\cos (x - y) = \frac{61 - 53}{14} = \frac{8}{14} = \frac{4}{7}