4. If cosec x + cotx = 11/2, then find the value of tan x.
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Cosecx + cotx = 11/2 [given ]------1)
•°•cosec²x -cot²x =1
= (cosecx - cotx )(cosecx+cotx) = 1
=>cosecx - cotx ×11/2 =1
=> cosecx - cotx = 2/11 -------2)
substracting 2)from 1)
cosecx-cotx -(cosecx + cotx ) = 2/11 - 11/2
cosecx - cotx - cosecx - cotx = 4-121/22
- 2cotx = -117/22
cotx = 117/44
Cotx = 1/tanx = 117/11
•°•tanx = 44/117
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