Find the value of $\tan 5 ° \tan 25 ° \tan 30 ° \tan 45 ° \tan 65 ° \tan 85 °$ .

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Solution

Find the value of $\tan 5 ° \tan 25 ° \tan 30 ° \tan 45 ° \tan 65 ° \tan 85 °$ .
$\begin{array}{rcl} \tan 5 ° \tan 25 ° \tan 30 ° \tan 45 ° \tan 65 ° \tan 85 ° & = & \tan 5 ° \tan 25 ° \tan 30 ° \times 1 \times \tan (90 ° - 25 °) \times \tan (90 ° - 5 °) \\ = & \tan 5 ° \times \tan 25 ° \times \tan 30 ° \times \cot 25 ° \times \cot 5 °; [\tan (90 ° - x) = \cot (x)] \\ = & (\tan 5 ° \times \cot 5 °) \times (\tan 25 ° \times \cot 25 °) \times \tan 30 ° \\ = & \tan 5 ° \times \tan 25 ° \times \tan 30 ° \times \frac{1}{\tan 25 °} \times \frac{1}{\tan 5 °}; [\tan (x) = \frac{1}{\cot (x)}] \\ = & 1 \times 1 \times \frac{1}{\sqrt{3}}; [\tan (30 °) = \frac{1}{\sqrt{3}}] \\ = & \frac{1}{\sqrt{3}} \end{array}$
Hence, the final value of the expression is $\frac{1}{\sqrt{3}}$ .

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5 + 15 + 25 + 35 + 45 + 55 + 65 + 75 + 85 + 95 = ___

Q. Evaluate tan 5 tan 25 tan 30 tan 65 tan 85.

Calculate the mode of the following data:

Class-interval	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$
Frequency	$5$	$4$	$7$	$12$	$8$	$1$	$4$

Let N = $\frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{3^{5} + 3^{5} + 3^{5}} \cdot \frac{6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}}$ then the value of ${log}_{2} N$ =

Q. Let

N = \frac{4^{5} + 4^{5} + 4^{5} + 4^{5}}{3^{5} + 3^{5} + 3^{5}} . \frac{6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5} + 6^{5}}{2^{5} + 2^{5}}

, then the value of

{log}_{2} N =

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Find the value of tan5°tan25°tan30°tan45°tan65°tan85°.

Find the value of $\tan 5 ° \tan 25 ° \tan 30 ° \tan 45 ° \tan 65 ° \tan 85 °$ .