If 3 tan θ = 4, then what is the value of 7 sinθ - 2 cos θ ?

3 tan θ = 4

tan θ = \(\frac{4}{3}\)

{ we know, tan θ = \(\frac{P}{B}\) }

By using pythagoras theorem,

P² + B² = H²

4² + 3² = H²

H = 5

Now,

7 sinθ - 2 cos θ

= 7 × \(\frac{4}{5}\) - 2 × \(\frac{3}{5}\)

= \(\frac{28}{5}\) -  \(\frac{6}{5}\)

= \(\frac{22}{5}\)