How do you simplify 1/sin x?

We need to simplify 1/sin x. Before simplifying first let us know what sine is.

Sine function

The sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right angled triangle.

sin x = opposite/hypotenuse

1/sin x = 1 / opposite/hypotenuse

= hypotenuse / opposite

We know that cosec x = hypotenuse / opposite

Hence 1/sin x = cosec x

Answer

1/sinx = cosec x

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