Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
[tex]3\:sinA+4\:cosA=5[/tex]
[tex]\frac{4}{5}\:cosA=1-\frac{3}{5}sinA[/tex]
Taking square on both sides
[tex]\left(\frac{4}{5}\:cosA\right)^2=\left(1-\frac{3}{5}sinA\right)^2[/tex]
[tex]16\:Cos^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A[/tex]
[tex]16\:-\:16\:Sin^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A[/tex]
[tex]25\:Sin^2\:A\:\:-\:30\:Sin\:A\:+\:9\:=\:0[/tex]
so the equation can further be easily solved
[tex]\sin \:A=\frac{3}{5}[/tex] ∵ [tex]sin A =[/tex] [ [tex]30[/tex] +- √(900 - 900) ] ÷ 50
