Question

among
$3 sinx + 5cosx = 5cosx = 5thenfind{3cosx - 5sinx}2$
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Answer 1

Answer:

3

Explanation:

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