The number of solutions of $$|\cos x|=\sin x$$, such that $$-4 \pi \leq x \leq 4 \pi$$ is :
A tower PQ stands on a horizontal ground with base $$Q$$ on the ground. The point $$R$$ divides the tower in two parts such that $$Q R=15 \mathrm{~m}$$. If from a point $$A$$ on the ground the angle of elevation of $$R$$ is $$60^{\circ}$$ and the part $$P R$$ of the tower subtends an angle of $$15^{\circ}$$ at $$A$$, then the height of the tower is :
Which of the following statements is a tautology ?
Let $$A=\left(\begin{array}{rrr}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right)$$ and $$B=A-I$$. If $$\omega=\frac{\sqrt{3} i-1}{2}$$, then the number of elements in the $$\operatorname{set}\left\{n \in\{1,2, \ldots, 100\}: A^{n}+(\omega B)^{n}=A+B\right\}$$ is equal to ____________.