Question

Evaluate:
tan 5° tan 25° tan 30° tan 65° tan 85º.​

Answer 1

Step-by-step explanation:

Evaluate:

tan 5° tan 25° tan 30° tan 65° tan 85º.

Answer 2

Step-by-step explanation:

Answer:

The value of tan 5° tan 25° tan 30° tan 65° tan 85º is 1/√3.

To find:

$The value of \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \tan 65 ^ { \circ } \tan 85 ^ { \circ }$

Solution:

Given,

$\tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \tan 65 ^ { \circ } \tan 85 ^ { \circ }$

$\begin{gathered}\begin{array} { c } { = \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \tan ( 90 - 65 ) ^ { \circ } \tan ( 90 - 85 ) ^ { \circ } } \\\\ { = \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \cot 25 ^ { \circ } \cot 5 ^ { \circ } } \\ { [ \because \tan ( 90 - x ) = \cot x ] } \\\\ { = \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \frac { 1 } { \tan 25 ^ { \circ } } \frac { 1 } { \tan 5 ^ { \circ } } } \\ { = \tan 30 ^ { \circ } = \frac { 1 } { \sqrt { 3 } } } \end{array}\end{gathered}$

$Hence, the value of \tan 5 ^ { \circ } \tan 25 ^ { \circ } \tan 30 ^ { \circ } \tan 65 ^ { \circ } \tan 85 ^ { \circ } \: </p><p> is \: \frac{1}{\sqrt3} </p><p></p><p>$