number of real solutions of the equation `|cotx|= cotx + 1/ sin x` `(0

1.	number of real solutions of the equation `\|cotx\|= cotx + 1/ sin x` `(0
Answer» `\|cotx\| = cotx +1/sinx` `cotx` will be positive when `x in (0,pi/2)`. `:. x in (0,pi/2)`, `cotx = cotx +1/sinx` `=>1/sinx = 0` `=>sinx = oo` We know, maximum value of `sin x` is `1.` So, no solution possible when `x in (0,pi/2)`. `cotx` will be negative when `x in (pi/2,pi)`. `:. x in (pi/2,pi)`, `-cotx = cotx +1/sinx` `=>-2cotx = 1/sinx` `=>-2cosx/sinx = 1/sinx` `=>cosx = -1/2` `=>x = (2pi)/3` So, `x = (2pi)/3` is the only solution available for the given equation. `:.` Number of solutions for this equation is `1`.

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number of real solutions of the equation `|cotx|= cotx + 1/ sin x` `(0

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