If $\sin \left(6\mathrm{\theta }\right) = 32{\cos }^5\left(\mathrm{\theta }\right)\sin \left(\mathrm{\theta }\right) - 32{\cos }^3\left(\mathrm{\theta }\right)\sin \left(\mathrm{\theta }\right) + 3\mathrm{x}$, then x is equal to :

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

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

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

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

$\mathrm{The} \mathrm{period} \mathrm{of} \mathrm{the} \mathrm{function} \mathrm{f}\left(\mathrm{\theta }\right) = \sin \left(\frac{\mathrm{\theta }}{3}\right) + \cos \left(\frac{\mathrm{\theta }}{2}\right) \mathrm{is}$

• $3\mathrm{\pi }$

• $6\mathrm{\pi }$

• $9\mathrm{\pi }$

• $12\mathrm{\pi }$

203.

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

• 0

• $\frac{1}{2}$

• 1

• $4\cos \left(\mathrm{\alpha }\right)\cos \left(\mathrm{\beta }\right)\cos \left(\mathrm{\gamma }\right)$

$\mathrm{The} \mathrm{value} \mathrm{of} \cos \left(\frac{2\mathrm{\pi }}{15}\right)\cos \left(\frac{4\mathrm{\pi }}{15}\right)\cos \left(\frac{8\mathrm{\pi }}{15}\right)\cos \left(\frac{14\mathrm{\pi }}{15}\right) \mathrm{is} :$

• $\frac{1}{16}$

• $\frac{1}{8}$

• $\frac{1}{12}$

• $\frac{1}{4}$

If A + B + C = 270°, then
cos(2A) + cos(2B) + cos(2C) is equal to :

• 4sin(A)sin(B)sin(C)

• 4cos(A)cos(B)cos(C)

• 1 - 4sin(A)sin(B)sin(C)

• 1 - 4cos(A)cos(B)cos(C)

If ${\mathrm{x}}_{\mathrm{n}} = \cos \left(\frac{\mathrm{\pi }}{2^{\mathrm{n}}}\right) + \mathrm{isin}\left(\frac{\mathrm{\pi }}{2^{\mathrm{n}}}\right)$, then $\prod _{\mathrm{n} = 1}^{\infty }$xⁿ is equal to

• - 1

• 1

• $\frac{1}{\sqrt{2}}$

• - 3

If n $\in$ N and the period of $\frac{\cos \left(\mathrm{n\pi }\right)}{\sin \left({\displaystyle \frac{\mathrm{x}}{\mathrm{n}}}\right)}$ is 4$\mathrm{\pi }$, then n is equal to

• 4

• 3

• 2

• 1

$\mathrm{The} \mathrm{expression} \mathrm{for} \tan \left(9°\right) - \tan \left(27°\right) - \tan \left(63°\right) + \tan \left(81°\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• 4

• 3

• 2

• 1

$\mathrm{In} ∆\mathrm{ABC}, \cos \left(\frac{\mathrm{B} + 2\mathrm{C} + 3\mathrm{A}}{2}\right) + \cos \left(\frac{\mathrm{A} - \mathrm{B}}{2}\right) \mathrm{is}$

• - 1

• 0

• 1

• 2

$\mathrm{The} \mathrm{value} \mathrm{of} \mathrm{series} \cos \left(12°\right) + \cos \left(84°\right) + \cos \left(132°\right) + \cos \left(156°\right) \mathrm{is}$

• $\frac{1}{2}$

• $\frac{1}{4}$

• $- \frac{1}{4}$

• $- \frac{1}{2}$