Question
$\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)=$ ________.
✓
Answer
$\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)=$ $\frac{5}{2}$ Solution: $\Rightarrow\frac{3\cot40^\circ}{\tan50^\circ}-\frac{1}{2}\Big(\frac{\cos35^\circ}{\sin55^\circ}\Big)$ $\Rightarrow\frac{3\cot(90^\circ-40^\circ)}{\tan50^\circ}-\frac{\cot35^\circ}{2\sin(90^\circ-55^\circ)}$ $\Rightarrow\frac{3\tan50^\circ}{\tan50^\circ}-\frac{\cot35^\circ}{2\cot35^\circ}$ $\Rightarrow3-\frac{1}{2}$ $\Rightarrow\frac{6-1}{2}$$\Rightarrow\frac{5}{2}$
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