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if 3sin0+5cos0=5,then write the value of 5sin0-3cos0=? 0=theta

if 3sin0+5cos0=5,then write the value of 5sin0-3cos0=?
0=theta

Grade:11

1 Answers

Arun
25757 Points
5 years ago
I have assumed theta as x
 
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

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