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Write the reciprocal of cosec θ.

May 9, 2026Mathematics

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Answer

\sin \theta

4 steps

4. Write the reciprocal of $\text{cosec } \theta$ .

Understand the definition of a reciprocal.
The reciprocal of a number or function is 1 divided by that number or function.
So, the reciprocal of $\text{cosec } \theta$ is $\frac{1}{\text{cosec } \theta}$ .
Recall the fundamental trigonometric identity for $\text{cosec } \theta$ .
The cosecant function is defined as the reciprocal of the sine function:
$\text{cosec } \theta = \frac{1}{\sin \theta}$
Substitute this identity into the reciprocal expression.
$\frac{1}{\text{cosec } \theta} = \frac{1}{\frac{1}{\sin \theta}}$
Simplify the expression.
$\frac{1}{\frac{1}{\sin \theta}} = 1 \times \frac{\sin \theta}{1} = \sin \theta$
The reciprocal of $\text{cosec } \theta$ is $\boxed{\sin \theta}$ .

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