Question

if 3 Sin A = 4 Cos A find the numerical value of Cos A

Answer 1

3 Sin A = 4 Cos A
=> cosA= (¾)(sinA)
=> cos²A= (9/16)(sin²A)
=> cos²A= (9/16)(1-cos²A)
=> cos²A= 9/16 - (9/16)cos²A
=> cos²A +(9/16)cos²A=9/16
=> cos²A[1+(9/16)]= 9/16
=> (25/16)cos²A=9/16
=> cos²A = (9/16)×(16×25)
=> cos²A = (9/25)
=> cosA = (3/5)
or...
=> cosA = -(3/5)