Question

If 3sinx+5cosx=5 then find the value of 5sinx-3cosx

Answer 1

heya...!!!!

3sinx + 5cosx = 5

=> (3sinx + 5cosx)² = 5²

=> 9sin²x + 25cos²x + 30sinxcosx = 25

=> 9sin²x + 9cos²x + 16cos²x + 30sinxcosx = 25

=> 9(sin²x + cos²x) + 16cos²x + 30sinxcosx = 25

=> 9 + 16cos²x + 30sinxcosx = 25

=> 16cos²x + 30sinxcosx - 16 = 0

=> 8cos²x + 15sinxcosx - 8 = 0

=> 8(1 - sin²x) + 15sinxcosx - 8 = 0

=> 8 - 8sin²x + 15sinxcosx - 8 = 0

=> 15sinxcosx - 8sin²x = 0

=> 15cosx = 8sinx

=> tanx = 15/8

secx = √(1 + tan²x)

=> secx = √(1 + 225/64)

=> secx = √289/64

=> secx = 17/8 = 1/cosx

=> cosx = 8/17

sinx = √1 - cos²x)

=> sinx = √(1 - 64/289)

=> sinx = √(289 - 64)/289

=> sinx = √225/289

=> sinx = 15/17

now,

5sinx - 3cosx

=> 5×15/17 - 3×8/17

=> 75/17 - 24/17

=> 51/17

=> 3

Answer 2

Answer:Plusminus 3

Step-by-step explanation: