If 5 tan θ – 4 = 0, then the value of 5sinθ - 4cosθ/5sinθ + 4 cosθ is A. 5/3 B. 5/6 C. 0 D. 1/6

Question

If 5 tan θ – 4 = 0, then the value of  \(\frac{5sinθ - 4cosθ}{5sinθ + 4 cosθ}\) is 

A. 5/3 

B.  5/6  

C. 0 

D. 1/6

Answer 1

Given, 

5 tan θ – 4 = 0 

So, 

5 tan θ = 4 

tan θ = 4/5 

In ∆ ABC, 

AC² = AB² + BC² 

AC² = (4)² + (5)² 

AC² = 16 + 25 

AC² = 41 

AC = √41 

Therefore, sin θ = AB/AC = 4/√41 

cos θ = BC/AC = 5/√41 

Now,