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Trigonometric Ratios — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Ratios2 Marks
Question
Prove that:$\tan20^\circ\tan35^\circ\tan45^\circ\tan55^\circ\tan70^\circ=1$
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Answer

$\tan20^\circ=\tan(90^\circ-70^\circ)=\cot70^\circ$
$\tan35^\circ=\tan(90^\circ-55^\circ)=\cot55^\circ$
$\tan45^\circ=1$
$\Rightarrow\cot70^\circ\tan70^\circ\times\cot55^\circ\tan55^\circ\tan45^\circ$
$\Rightarrow1\times1\times1=1$
Hence proved.

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