If \(\frac{3}{\sqrt {3}}\)cotθ=1, then find the value of \(\frac{2-sin^2θ}{1-cos^2θ}\)+(cosec2θ-secθ)
Answer & explanation
Correct answer: option 3
\(\frac{3}{\sqrt {3}}\)cotθ=1
\(\frac{\sqrt {3}×\sqrt {3}}{\sqrt {3}}\)cotθ=1
cotθ=\(\frac{1}{\sqrt {3}}\)=60°
⇒ \(\frac{2-sin^2θ}{1-cos^2θ}\)+(cosec2θ-secθ) = \(\frac{2-(\frac{\sqrt {3}}{2})^2}{1-(\frac{1}{2})^2}\)+(\(\frac{2}{\sqrt {3}}\))2-2
⇒ \(\frac{2-\frac{3}{4}}{1-\frac{1}{4}}\)+\(\frac{4}{3}\)-\(\frac{2}{3}\)
⇒ \(\frac{\frac{5}{4}}{\frac{3}{4}}\)+[\(\frac{4}{3}\)-\(\frac{2}{3}\)]
= 1