Trigonometrical Ratios And Identities Ques 25
Match the conditions/expressions in Column I with values in Column II.
$(\sin 3 \alpha) /(\cos 2 \alpha)$ 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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Answer:
Correct Answer: 25.$(A \rightarrow r; B \rightarrow p )$
Solution:
Formula:
Domain and Range of Trigonometric Functions:
- 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 $A \rightarrow r$.
BETA
