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If the equation tan (P cot x)=cot (P tan...

If the equation `tan (P cot x)=cot (P tan x)` has a solution in `x in (0, pi)-{pi/2}`, then prove that `P le pi/4`.

Text Solution

Verified by Experts

`tan (P cot x)=cot (P tan x)`
or `tan (P cot x)= tan (pi/2 - P tan x)`
or `P cot x=pi/2-P tan x`
or `P(tan x+ cot x) = pi/2` where `P gt 0`
Now. `tan x+ cot x ge 2`
or `2P le P (tan x+ cot x) = pi/2 or P le pi/4`
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