Question

If 3 sinA+4 cosA=5 then prove that:sinA=3/5.​

Answer 1

Please check the explanation.

Explanation:

Given the expression

`3\:sinA+4\:cosA=5`

`(4)/(5)\:cosA=1-(3)/(5)sinA`

Taking square on both sides

`\left((4)/(5)\:cosA\right)^2=\left(1-(3)/(5)sinA\right)^2`

`16\:Cos^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A`

`16\:-\:16\:Sin^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A`

`25\:Sin^2\:A\:\:-\:30\:Sin\:A\:+\:9\:=\:0`

so the equation can further be easily solved

`\sin \:A=(3)/(5)` ∵
`sin A =` [
`30` +- √(900 - 900) ] ÷ 50