If $\sec \theta = x + \frac{1}{4x}$ where $0^{\circ} < \theta < 90^{\circ}$,then $\sec \theta + \tan \theta$ is equal to:

If $\tan A = n \tan B$ and $\sin A = m \sin B ,$ then the value of $\cos ^{2} A$ is

The minimum value of $9\tan^2\theta + 4\cot^2\theta$ is

$A$ circular wire of diameter $10\,cm$ is cut and placed along the circumference of a circle of diameter $1\,m$. The angle subtended by the wire at the centre of the circle is equal to

If $\theta$ is eliminated from the equations $x = a \cos(\theta - \alpha)$ and $y = b \cos(\theta - \beta)$,then $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{2xy}{ab} \cos(\alpha - \beta)$ is equal to

If $7 \sin^{2} \theta + 3 \cos^{2} \theta = 4$,then the value of $\tan \theta$ is (where $\theta$ is acute).