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Rina8888 [55]
3 years ago
5

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

Mathematics
1 answer:
lutik1710 [3]3 years ago
7 0

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

3\:sinA+4\:cosA=5

\frac{4}{5}\:cosA=1-\frac{3}{5}sinA

Taking square on both sides

\left(\frac{4}{5}\:cosA\right)^2=\left(1-\frac{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=\frac{3}{5}         ∵ sin A = [ 30 +- √(900 - 900) ] ÷ 50

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