If $(\cos \theta + \sin \theta) : (\cos \theta - \sin \theta) = (\sqrt{3} + 1) : (\sqrt{3} - 1), 0^\circ < \theta < 90^\circ$, then what is the value of $\sec \theta$?
Answer & explanation
Correct answer: option 1
\(\frac{cosθ + sinθ}{cosθ - sinθ}\) = \(\frac{√3+ 1}{√3- 1}\)
By applying componendo and dividendo ,
\(\frac{2cosθ }{2 sinθ}\) = \(\frac{2√3}{2}\)
cotθ = √3
{ using , cot30º = √3 }
Now,
secθ
= sec30º
= \(\frac{2}{√3}\)
= \(\frac{2√3}{3}\)