Question

al CALE
1. If 3 sin A + 5 cos A = 5 then show that 5 sin A -- 3 cos A = +3​

Answer 1

=> 3sinA + 5cosA = 5

Square on both sides:

=> (3sinA + 5cosA)² = 5²

=> 9sin²A + 25cos²A + 30sinAcosA = 25

=> 9(1 - cos²A) + 25(1 - sin²A) + 30sinAcosA = 25

=> 9 - 9cos²A + 25 - 25sin²A + 30sinAcosA = 25

=> - 9cos²A - 25sin²A + 30sinAcosA = - 9

=> 9 = 9cos²A + 25sin²A - 30sinAcosA

=> 9 = (3cosA)² + (5cosA)² - 30sinAcosA

=> 9 = (5sinA - 3cosA)²

=> √9 = 5sinA - 3cosA

=> ± 3 = 5sinA - 3cosA

Using: sin²A = 1 - cos²A

cos²A = 1 - sin²A