Mathematics : Trigonometric Functions

• $\frac{56}{33}$

• $\frac{33}{56}$

• $\frac{16}{65}$

• $\frac{60}{61}$

$\sum _{\mathrm{k} = 1}^3 {\cos }^2\left(\left(2\mathrm{k} - 1\right)\frac{\mathrm{\pi }}{12}\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• 0

• $\frac{1}{2}$

• $- \frac{1}{2}$

• $\frac{3}{2}$

$\mathrm{If} \frac{3 + 2\mathrm{isin}\left(\mathrm{\theta }\right)}{1 - 2\mathrm{isin}\left(\mathrm{\theta }\right)} \mathrm{is} \mathrm{a} \mathrm{real} \mathrm{number} \mathrm{and} 0 < \mathrm{\theta } < 2\mathrm{\pi }, \mathrm{then} \mathrm{\theta } \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

${\cos }^2\left(76°\right) + {\cos }^2\left(16°\right) - \cos \left(76°\right)\cos \left(16°\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• 0

• $\frac{1}{2}$

• $-\frac{1}{ 2}$

• $\frac{3}{4}$

$\sinh \left(\mathrm{ix}\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\mathrm{isin}\left(\mathrm{x}\right)$

• $\sin \left(\mathrm{ix}\right)$

• $- \mathrm{isin}\left(\mathrm{x}\right)$

• $\mathrm{isin}\left(\mathrm{ix}\right)$

The perimeter of a triangle is 16cm, one of the sides is of length 6cm. If the area of the triangle is 12 sq cm. Then the triangle is

• right angled

• isosceles

• equilateral

• scalene

If $∆$ABC is right angled at A, then r₂ + r₃ is equal to

• r₁ - r

• r₁ + r

• r - r₁

• R

If in $∆\mathrm{ABC}$, r₁ < r₂ < r₃, then :

• a < b < c

• a > b > c

• b > a < c

• a < c < b

In a $∆\mathrm{ABC}$, if 3a = b + c, then $\cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)$ is equal to :

• 1

• 2

• 3

• 4

If in a triangle, if b = 20, c = 21 and $\sin \left(\mathrm{A}\right) = \frac{3}{5}$, then a is equal to

• 12

• 13

• 14

• 15