\(\dfrac{\tan 47^\circ}{\cot 43^\circ}=1\). Write ‘True’ or ‘False’ and justify.
True.
Step 1: Recall the relation between cotangent and tangent:
\(\cot \theta = \tan(90^\circ - \theta)\).
Step 2: Put \(\theta = 43^\circ\).
So, \(\cot 43^\circ = \tan(90^\circ - 43^\circ)\).
Step 3: Simplify inside the bracket:
\(90^\circ - 43^\circ = 47^\circ\).
So, \(\cot 43^\circ = \tan 47^\circ\).
Step 4: Now substitute this result into the given expression:
\(\dfrac{\tan 47^\circ}{\cot 43^\circ} = \dfrac{\tan 47^\circ}{\tan 47^\circ}\).
Step 5: Anything divided by itself is 1 (except zero).
So, \(\dfrac{\tan 47^\circ}{\tan 47^\circ} = 1\).
Final Answer: The statement is True.