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Tan5° tan25° tan30° tan65°tan85° =1/ root …

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Tan5° tan25° tan30° tan65°tan85° =1/ root 3

Posted by Suraj Nayak 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

We have,
tan 5° tan 25° tan 30° tan 65° tan 85°
= (tan 5° tan 85°) (tan 25° tan 65°) tan 30° {tex}\left[ \begin{array} { c } { \because \tan 85 ^ { \circ } = \tan \left( 90 ^ { \circ } - 5 ^ { \circ } \right) = \cot 5 ^ { \circ } } \\ { \tan 65 ^ { \circ } = \tan \left( 90 ^ { \circ } - 25 ^ { \circ } \right) = \cot 25 ^ { \circ } } \end{array} \right] {/tex}
= (tan 5° cot 5°) (tan 25° cot 25°) tan 30°

={tex}\left(tan5^\circ\times\frac1{\tan5^\circ}\right)\left(tan25^\circ\times\frac1{\tan25^\circ}\right){/tex} {tex}\left[cot\theta=\frac1{\tan\theta}\right]{/tex}
{tex}= 1 \times 1 \times \frac { 1 } { \sqrt { 3 } } = \frac { 1 } { \sqrt { 3 } } {/tex}

1Thank You

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