Find the value of \tan 35^{\circ} \cot 40^{\circ} \tan 45^{\circ} \cot 50^{\circ} \tan 55^{\circ}.

SSC CGL 20 Aug 2021 Shift 1 Paper

Question : 62 of 100

Marks: +1, -0

Find the value of

\tan 35^{∘} \cot 40^{∘} \tan 45^{∘} \cot 50^{∘} \tan 55^{∘}

Solution:

\tan 35^{∘} \cot 40^{∘} \tan 45^{∘} \cot 50^{∘} \tan 55^{∘}

=\tan (90^{∘}-55^{∘}) × \cot 40^{∘}

× \tan 45^{∘} × \cot (90^{∘}-40^{∘}) × \tan 55^{∘}

=\cot 55^{∘} × \cot 40^{∘} × \tan 45^{∘}

× \tan 40^{∘} × \tan 55^{∘}

=\;{1}/{\tan 55^{∘}} × \tan 55^{∘} × \;{1}/{\tan 40^{∘}}

× \tan 40^{∘} × \tan 45^{∘}

=\tan 45^{∘}=1

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