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if 4sinx+3cosx=7/5 then 3sinx+2cosx is equal to.............................?

if 4sinx+3cosx=7/5 then 3sinx+2cosx is equal to.............................?

Grade:11

1 Answers

praneethvikram
46 Points
6 years ago
4 sinx + 3 cosx = 7/5
let 4cosx-3sinx = p
now square both of them and add
=> 16 (sin^2x+cos^2x)  + 9 (sin^2x + cos^2x) = p^2 + 49/25
=> 25 = p^2 + 49/25
=> p^2 = 576/25 = > p = 24/5
now 
4sinx + 3cosx = 7/5
4 cosx – 3sinx = 24/5
now solving them we get
sinx = -79/25  cosx =117/25
 
=> 3 sinx + 2 cosx =    ( 3 * -79 + 2 * 117 ) / 25   = -3 / 25
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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