Question

find the minimum value of cosec theta

Answer 1

See this it may be helpfull

Answer 2

minimum value of cosecθ tends to -∞

okay, we have to find the minimum value of cosecθ

as you know, cosecθ is the reciprocal of sinθ.

and range of sinθ ∈ [ -1, 1]

means, -1 ≤ sinθ ≤ 1

but you know, cosecθ is undefined at 0°, 180°, 270°, ...

so, in range of cosecθ isn't included (-1, 1) values. because cosecθ will be undefined in this range.

range of cosecθ ∈ R - (-1, 1)

so, cosecθ ∈ (-∞, -1] U [1, ∞ )

then, minimum value of cosecθ tends to -∞

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