Question

if 13 sin A =5then evaluate 5sinA -2cosA/tanA​

Answer 1

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3sinA + 5cosA = 5

(3sinA + 5cosA)^2 = 5^2

9sin^2 A + 25cos^2 A + 30sinAcosA = 25

9(1-cos^2) + 25(1-sin^2) + 30sinAcosA = 25

9 - 9cos^2 + 25 - 25sin^2 + 30sinAcosA = 25

9 = 9cos^2 + 25sin^2 - 30sinAcosA

(5sinA - 3cosA)^2=9

5sinA -3cosA = 3