Question

3 sin x + 5 cos x=5 then 5 sin x - 3 cos x =

Answer 1

3sinx + 5cosx = 5

squaring both sides

9sin ^ 2x + 25 cos ^2x+30sinx cosx = 25

9 + 16cos^ 2x +30sinxcosx = 25

16cos^2x+30sinxcosx = 16

30sinxcosx = 16sin^2x

30sinxcosx - 16sin^2x = 0

sinx(30cosx - 16sinx) = 0

either sinx = 0 or tanx = 15/8

1) sinx = 0

cosx =1

5sinx-3cosx = -3

2) tanx = 15/8

5*15 /17 - 3 *8/17 =3

51/17= 3

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