Question

Solve , 5cosx-3sinx=5 .

Answer 1

\[\frac{\sqrt{5^2 + 3^2} \left(5 \cos{x} - 3\sin{x}\right)}{\sqrt{5^2 + 3^2}}=5\]
\[\cos \alpha = \frac{5}{\sqrt{5^2 + 3^2}}, \sin \alpha = \frac{3}{\sqrt{5^2 + 3^2}}\]
\[\cos \alpha \cos x - \sin \alpha \sin x = \frac{5}{\sqrt{5^2 + 3^2}} \]

\[cos \left( \alpha + x\right) = \frac{5}{\sqrt{5^2+3^2}}\]

Answer 2

\[x = \cos^{-1} \frac{5}{5^2 + 3^2} - \alpha\]