Question

3sinx+5cosx=5 so what is the value of 5sinx-3cosx

Answer 1

Hmm... Let me identify...

3sinx +5cosx=5

squaring both siods

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

sinx=15/17 and cosx =8/17

5sinx-3cosx=

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

51/17=3

So thanks for asking.