Trigonometrical Ratios and Identities 1 Question 22

22. $(\sin 3 \alpha) /(\cos 2 \alpha)$ is

$(1992,2 M)$

Column I Column II
A. positive p. $(13 \pi / 48,14 \pi / 48)$
B. negative q. $(14 \pi / 48,18 \pi / 48)$
r. $(18 \pi / 48,23 \pi / 48)$
s. $(0, \pi / 2)$

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Solution:

  1. In the interval $\frac{13 \pi}{48}, \frac{14 \pi}{48}, \cos 2 \alpha<0$ and $\sin 3 \alpha>0$. $\Rightarrow \frac{\sin 3 \alpha}{\cos 2 \alpha}$ is negative, therefore $B \rightarrow p$.

Again, in the interval $\frac{18 \pi}{48}, \frac{23 \pi}{48}$, both $\sin 3 \alpha$ and $\cos 2 \alpha$ are negative, so $\frac{\sin 3 \alpha}{\cos 2 \alpha}$ is positive, therefore $A \rightarrow r$.



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