The equivalent fraction is [tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex].
The given expression is tan 40°-tan 10°/1+tan 40°.tan 10°.
When simplifying trigonometric expressions, one approach is to change everything into sine or cosine.
Now, [tex]\frac{\frac{sin40\textdegree}{cos40\textdegree} -\frac{sin10\textdegree}{cos10\textdegree}}{1+\frac{sin40\textdegree}{cos40\textdegree} .\frac{sin10\textdegree}{cos10\textdegree} }[/tex]
=[tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex]
Therefore, the equivalent fraction is [tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex].
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