If 3sinθ = 2cos²θ, 0° < θ < 90°, then the value of (tan²θ + sec²θ - cosec²θ) is:

Solution (By Examveda Team)

$$\eqalign{ & 3\sin \theta = 2{\cos ^2}\theta \cr & {\text{Let }}\theta = {30^ \circ } \cr & 3 \times \frac{1}{2} = 2 \times \frac{{{{\left( {\sqrt 3 } \right)}^2}}}{4} \cr & \frac{3}{2} = \frac{3}{2} \cr & {\tan ^2}\theta + {\sec ^2}\theta - {\text{cose}}{{\text{c}}^2}\theta \cr & = {\tan ^2}{30^ \circ } + {\sec ^2}{30^ \circ } - {\text{cose}}{{\text{c}}^2}{30^ \circ } \cr & = \frac{1}{3} + \frac{4}{3} - 4 \cr & = \frac{5}{3} - 4 \cr & = - \frac{7}{3} \cr} $$