If \(\frac{cosθ+sinθ}{cosθ-sinθ}\) = \(\frac{\sqrt {3}+1}{\sqrt {3}-1}\), 0° < θ < 90°, then find the value of secθ.
Answer & explanation
Correct answer: option 4
\(\frac{cosθ+sinθ}{cosθ-sinθ}\) = \(\frac{\sqrt {3}+1}{\sqrt {3}-1}\)
By componendo & dividendo concept
\(\frac{cosθ}{sinθ}\)=\(\frac{\sqrt {3}}{1}\)
cotθ = \(\sqrt {3}\) = 30°
Now, secθ =\(\frac{2}{\sqrt {3}}\)×\(\frac{\sqrt {3}}{\sqrt {3}}\)
= \(\frac{2\sqrt {3}}{3}\)