$\mathrm{What} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} \tan \left(75°\right) + \cot \left(75°\right)$

• 2

• 4

• $2\sqrt{3}$

• $4\sqrt{3}$

What is the value of $\cos \left(46°\right)\cos \left(47°\right)\cos \left(48°\right)\cos \left(49°\right)\cos \left(50°\right) ... \cos \left(135°\right) = ?$

•  - 1

• 0

• 1

• Greater than 1

$\mathrm{If} \sin \left(2\mathrm{\theta }\right) = \cos \left(3\mathrm{\theta }\right), \mathrm{where} 0 < \mathrm{\theta } < \frac{\mathrm{\pi }}{2}, \mathrm{then} \mathrm{what} \mathrm{is} \sin \left(\mathrm{\theta }\right) = ?$

• $\frac{\sqrt{5} + 1}{4}$

• $\frac{\sqrt{5} - 1}{4}$

• $\frac{\sqrt{5} + 1}{16}$

• $\frac{\sqrt{5} - 1}{16}$

14.

If the roots of the equation x² + px + q = 0 are tan(19⁰) and tan(26°), then which one of the following is correct?

• q - p = 1

• p - q = 1

• p + q = 2

• p + q = 3

what is ${\left(1 + \tan \left(\mathrm{\alpha }\right)\tan \left(\mathrm{\beta }\right)\right)}^2 + {\left(\tan \left(\mathrm{\alpha }\right) - \tan \left(\mathrm{\beta }\right)\right)}^2 - {\sec }^2\left(\mathrm{\alpha }\right){\sec }^2\left(\mathrm{\beta }\right) = ?$

• 0

• 1

• 2

• 4

If $\mathrm{p} = \csc \left(\mathrm{\theta }\right) - \cot \left(\mathrm{\theta }\right) \mathrm{and} \mathrm{q} = {\left(\csc \left(\mathrm{\theta }\right) - \cot \left(\mathrm{\theta }\right)\right)}^{ - 1}$, then which one of the following is correct?

• pq = 1

• p = q

• p + q = 1

• p + q = 0

What is the least value of 25cosec²(x) + 36sec²(x) ?

• 1

• 11

• 120

• 121

$\mathrm{If} \sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right) = \sqrt{2}\cos \left(\mathrm{\theta }\right), \mathrm{then} \mathrm{what} \mathrm{is} \left(\cos \left(\mathrm{\theta }\right) - \sin \left(\mathrm{\theta }\right)\right) = ?$

• $- \sqrt{2}\cos \left(\mathrm{\theta }\right)$

• $- \sqrt{2}\sin \left(\mathrm{\theta }\right)$

• $\sqrt{2}\sin \left(\mathrm{\theta }\right)$

• $2\sin \left(\mathrm{\theta }\right)$

$\mathrm{If} \sin \left(\mathrm{\theta }\right) = - \frac{1}{2} \mathrm{and} \tan \left(\mathrm{\theta }\right) = \frac{1}{\sqrt{3}}, \mathrm{Then} \mathrm{in} \mathrm{which} \mathrm{quadrant} \mathrm{does} \mathrm{\theta } \mathrm{lie} ?$

• First

• Second

• Third

• Fourth

$$\begin{gathered} \mathrm{If} \sin \left(\mathrm{x}\right) = \frac{1}{\sqrt{5}}, \sin \left(\mathrm{y}\right) = \frac{1}{\sqrt{10}}, \mathrm{where} 0 < \mathrm{x} < \frac{\mathrm{\pi }}{2}, 0 < \mathrm{y} < \frac{\mathrm{\pi }}{2}, \\ \mathrm{then} \mathrm{what} \mathrm{is} \left(\mathrm{x} + \mathrm{y}\right) = ? \end{gathered}$$

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• 0