If $\frac{3\sqrt{3}secθ+4 tan θ}{3 tan θ + \sqrt{3} sec θ}=2, 0° < θ < 90°$, then the value of cos θ will be :
Answer & explanation
Correct answer: option 4
$\frac{3\sqrt{3}secθ+4 tan θ}{3 tan θ + \sqrt{3} sec θ}=2, 0° < θ < 90°$
3√3 secθ + 4 tanθ = 6 tanθ + 2√3 secθ
√3 secθ = 2 tanθ
cosec θ = \(\frac{2}{√3}\)
{ we know, cosec 60º = \(\frac{2}{√3}\) }
Now,
cosθ
= cos 60º
= \(\frac{1}{2}\)