If 7sin2 θ + 3cos2 θ = 4, 0 < θ < 90°, then the value of \(\frac{tan^2 2 θ - sin^2 θ}{cot θ + cosec2 θ}\)?
Answer & explanation
Correct answer: option 3
7sin² θ + 3cos² θ = 4
θ = 30° satisfies the equation
⇒ \(\frac{tan^2 2 θ - sin^2 θ}{cot θ + cosec2 θ}\) = \(\frac{tan^2 60° - sin^2 30°}{cot 30° + cosec 60°}\)
= \(\frac{3 -\frac{1}{4}}{\sqrt {3} + \frac{2}{\sqrt {3}}}\)
= \(\frac{\frac{11}{4}}{\frac{5}{\sqrt {3}}}\)
= \(\frac{11 \sqrt {3}}{20}\)