Question:
If 5 tan θ - 4 = 0, then the value of 5 sin θ - 4 cos θ
Answer:
Given 5*tanθ - 4 = 0
=> 5*tanθ = 4
=> tanθ = 4/5
Now in triangle ABC,
From Pythagoruse Theorem
AC2 = AB2 + BC2
=> AC2 = 42 + 52
=> AC2 = 16 + 25
=> AC2 = 41
=> AC = √41
Now 5* sin θ - 4* cos θ
= 5*(4/√41) - 4*(5/√41)
= 20/√41 - 20/√41
= 0
So 5* sin θ - 4* cos θ = 0
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