50.Simplify 𝑠𝑖𝑛(𝑥) 𝑐𝑜𝑠𝑒𝑐 (𝑥)

To simplify the expression \( \sin(x) \cdot \csc(x) \), we use the fact that the cosecant function is the reciprocal of the sine function:

\[
\csc(x) = \frac{1}{\sin(x)}
\]

Now substitute this into the expression:

\[
\sin(x) \cdot \csc(x) = \sin(x) \cdot \frac{1}{\sin(x)} = 1
\]

Thus, the simplified form of \( \sin(x) \cdot \csc(x) \) is:

\[
1
\]

Would you like further clarification on this,

Simplify the trigonometric expression sin(x) × cosec(x) using the reciprocal identity. This step-by-step guide explains how to reduce the expression to 1. Perfect for students in Grades 9-11 studying trigonometric functions and identities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation