What is $\cot \left(\mathrm{A}\right) + \csc \left(\mathrm{A}\right) = ?$

• $\tan \left(\frac{\mathrm{A}}{2}\right)$

• $\cot \left(\frac{\mathrm{A}}{2}\right)$

• $2\tan \left(\frac{\mathrm{A}}{2}\right)$

• $2\cot \left(\frac{\mathrm{A}}{2}\right)$

What is $\cot \left(\frac{\mathrm{A}}{2}\right) - \tan \left(\frac{\mathrm{A}}{2}\right)$ = ?

• tan(A)

• cot(A)

• 2tan(A)

• 2cot(A)

If angle C of a triangle ABC is a right angle, then what is tan(A ) + tan(B) equal to ?

• $\frac{{\mathrm{a}}^2 - {\mathrm{b}}^2}{\mathrm{ab}}$

• $\frac{{\mathrm{a}}^2}{\mathrm{bc}}$

• $\frac{{\mathrm{b}}^2}{\mathrm{ca}}$

• $\frac{{\mathrm{c}}^2}{\mathrm{ab}}$

What is $\cos \left(80°\right) + \cos \left(40°\right) - \cos \left(20°\right) = ?$

• 2

• 1

• 0

• - 19

If 2tan(A) = 3tan(B) = 1, then what is tan (A - B) equal to ?

• $\frac{1}{5}$

• $\frac{1}{6}$

• $\frac{1}{7}$

• $\frac{1}{9}$

$\mathrm{What} \mathrm{is} \sin (\mathrm{\alpha } + \mathrm{\beta }) - 2\sin \left(\mathrm{\alpha }\right)\cos \left(\mathrm{\beta }\right) + \sin (\mathrm{\alpha } - \mathrm{\beta }) \mathrm{equal} \mathrm{to} ?$

• 0

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

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

• $\sin \left(\mathrm{\alpha }\right) + \sin \left(\mathrm{\beta }\right)$

If tan(A) – tan(B) = x and cot(B) – cot(A) = y, then what is the value of cot(A - B) ?

• $\frac{{\displaystyle 1}}{{\displaystyle \mathrm{x}}} + \frac{{\displaystyle 1}}{{\displaystyle \mathrm{y}}}$

• $\frac{{\displaystyle 1}}{{\displaystyle \mathrm{y}}} - \frac{{\displaystyle 1}}{{\displaystyle \mathrm{x}}}$

• $\frac{\mathrm{xy}}{\mathrm{x} + \mathrm{y}}$

• $1 + \frac{1}{\mathrm{xy}}$

78.

What is the length of the chord of a unit circle which subtends an angle θ at the centre ?

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

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

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

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

Consider the following statements :

1) cos(θ) + sec(θ) can never be equal to 1.5

2) tan(θ) + cot(θ) can never be less than 2

Which of the above statements is/are correct ?

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

If $\mathrm{If} \csc \left(\mathrm{\theta }\right) = \frac{29}{21} \mathrm{where} 0 < \mathrm{\theta } < 90°, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{value} \mathrm{of} 4\sec \left(\mathrm{\theta }\right) + 4\tan \left(\mathrm{\theta }\right) = ?$

• 5

• 10

• 15

• 20