Simplify the equation:

\[
\frac{1-\sin^2x}{\cos x} = \frac{\sin 2x}{2\sin x}
\]

Left side:
1-sin²(x) = cos²(x)
1-sin²(x) / cos(x) = cos²(x) / cos(x) = cos(x)
Right side:
sin(2x) = 2 sin(x) cos(x)
sin(2x) / 2 sin(x) = 2 sin(x) cos(x) / 2 sin(x) = ***cos x ***

Answered by AL2006 | 2024-06-10

The equation simplifies to cos x = cos x , which is an identity valid for all x except where cos x = 0 . Both sides were reduced using trigonometric identities. This verification confirms that the equation holds true universally within its domain.
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Answered by AL2006 | 2024-10-13