https://file.aiquickdraw.com/mathbot/file/1727318547693t2cs6r8f.jpg

We are tasked with solving the equation given in the image:

\[
x \cdot \sin 45^\circ \cdot \tan 60^\circ = \frac{\sin 30^\circ \cdot \cot 30^\circ}{3 \cdot \cos 60^\circ \cdot \csc 45^\circ}
\]

Let’s begin by calculating the values of the trigonometric functions.

### Left-hand side (LHS):
\[
\sin 45^\circ = \frac{1}{\sqrt{2}}, \quad \tan 60^\circ = \sqrt{3}
\]
Thus, the LHS becomes:
\[
x \cdot \frac{1}{\sqrt{2}} \cdot \sqrt{3} = x \cdot \frac{\sqrt{3}}{\sqrt{2}}
\]

### Right-hand side (RHS):
1. \(\

If x sin(45°) tan(60°) = (sin(30°) cot(30°)) / (3 cos(60°) cosec(45°)), find x.

Learn how to solve the equation x sin(45°) tan(60°) = (sin(30°) cot(30°)) / (3 cos(60°) cosec(45°)) step by step using trigonometric identities and simplifications. This problem involves fundamental trigonometric concepts and is suitable for students in Grades 9-11.

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