Find the value of- tan 20- - tan 40-tan 50-tan 60- - tan 70-

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Relation between Trigonometric Ratios

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Find the value of: tan 20^o. tan 40^o. tan 50^o. tan 60^o. tan 70^o

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tan 10^{\circ} tan 20^{\circ} tan 30^{\circ} tan 40^{\circ} tan 50^{\circ} tan 60^{\circ} tan 70^{\circ} tan 80^{\circ}

\frac{2 sin 68^{\circ}}{cos 22^{\circ}} - \frac{2 cot 15^{\circ}}{5 tan 75^{\circ}} - \frac{3 tan 45^{\circ} tan 20^{\circ} tan 40^{\circ} tan 50^{\circ} tan 70^{\circ}}{5}

\frac{tan 70^{\circ} - tan 20^{\circ}}{tan 50^{\circ}}

\frac{2 sin 68^{\circ}}{cos 22^{\circ}} - \frac{2 cot 15^{\circ}}{5 tan 75^{\circ}} - \frac{3 tan 45^{\circ} tan 20^{\circ} tan 40^{\circ} tan 50^{\circ} tan 70^{\circ}}{5}

\frac{2}{3} (\cos^{4} 30 - \sin^{4} 45 °) - 3 (\sin^{2} 60 ° - \sec^{2} 45 °) + \frac{1}{4} \cot^{2} 30 °

4 (\sin^{4} 30 ° + \cos^{4} 60 °) - \frac{2}{3} (\sin^{2} 60 ° - \cos^{2} 45 °) + \frac{1}{2} \tan^{2} 60 °

\frac{\sin 50 °}{\cos 40 °} + \frac{cosec 40 °}{\sec 50 °} - 4 \cos 50 ° cosec 40 °

\frac{2 \sin 68 °}{\cos 22 °} - \frac{2 \cot 15 °}{5 \tan 75 °} - \frac{3 \tan 45 ° \tan 20 ° \tan 40 ° \tan 50 ° \tan 70 °}{5}

\frac{3 \cos 55 °}{7 \sin 35 °} - \frac{4 (\cos 70 ° cosec 20 °)}{7 (\tan 5 ° \tan 25 ° \tan 45 ° \tan 65 ° \tan 85 °)}

\frac{\sin 18 °}{\cos 72 °} + \sqrt{3} \{\tan 10 ° \tan 30 ° \tan 40 ° \tan 50 ° \tan 80 °\}

\frac{\cos 58 °}{\sin 32 °} + \frac{\sin 22 °}{\cos 68 °} - \frac{\cos 38 ° cosec 52 °}{\tan 18 ° \tan 35 ° \tan 60 ° \tan 72 ° \tan 55 °}

{(\frac{3 \tan 41 °}{\cot 49 °})}^{2} - {(\frac{\sin 35 ° \sec 55 °}{\tan 10 ° \tan 20 ° \tan 60 ° \tan 70 ° \tan 80 °})}^{2}

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