If $\frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, 0^\circ < \theta < 90^\circ$ then what is the value of $(\sec \theta + cosec \theta + \cot \theta)$?
Answer & explanation
Correct answer: option 4
\(\frac{cosθ}{1-sinθ}\) + \(\frac{cosθ}{1+sinθ}\) = 4
\(\frac{2cosθ}{1-sin²θ}\) = 4
{ sin²θ + cos²θ = 1 }
\(\frac{2cosθ}{cos²θ}\) = 4
secθ = 2
{ sec60º = 2 }
So, θ = 60º
Now,
secθ + cosecθ + cotθ
= sec60º + cosec60º + cot60º
= 2 + \(\frac{2}{√3}\) + \(\frac{1}{√3}\)
= 2 + √3