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Answer» 3Explanation: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 |
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