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Match the conditions/expressions in Colu...

Match the conditions/expressions in Column I with values in Column II
`(sin 3 alpha)//cos2 alpha)` is
`{:(" Column I"," Column II"),("A. Positive","p."(13pi//48, 14pi//48)),("B. negative","q."(14pi//48, 18pi//48)),(,"r."(18pi//48, 23pi//48)),(,"s."(0, pi//2)):}`

Text Solution

Verified by Experts

The correct Answer is:
A `rarr` r; B `rarr` p
In the interval `((13pi)/(48),(14pi)/(48)),cos2 alpha lt 0 and sin 3 alpha gt 0`. `implies(sin3alpha)/(cos2alpha)` is negative, therefore B `rarr` p.
Again in the interval `((18pi)/(48),(23pi)/(48))`, both `sin 2 alpha` and `cos 2 alpha` are negative, so `(sin 3 alpha)/(cos 2 alpha)` is positive, therefore A`rarr r.
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