Question
Evaluate:
$=\tan35^\circ \tan40 \tan50^\circ \tan55^\circ$
$=\tan35^\circ \tan40 \tan50^\circ \tan55^\circ$
✓
Answer
$ \tan35^\circ=\tan(90^\circ-55^\circ)=\cot55^\circ$
$ \tan40^\circ=\tan(90^\circ-50^\circ)=\cot+50^\circ$
$=\cot55^\circ\cdot\cot50^\circ\cdot\tan50^\circ\cdot\tan55^\circ$
$=\cot55^\circ\cdot\tan55^\circ\cdot\cot50^\circ\cdot\tan50^\circ$
$=1$
$ \tan40^\circ=\tan(90^\circ-50^\circ)=\cot+50^\circ$
$=\cot55^\circ\cdot\cot50^\circ\cdot\tan50^\circ\cdot\tan55^\circ$
$=\cot55^\circ\cdot\tan55^\circ\cdot\cot50^\circ\cdot\tan50^\circ$
$=1$
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