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JEE MainMathematicsEasyTrigonometry

The value of  tan20∘cot70∘\frac{tan20^{\circ}}{cot70^{\circ}} is equal
to.

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cot⁡(90∘−θ)=tan⁡θ\cot\left( 90^{\circ} - \theta \right) = \tan\theta
∴tan⁡20∘cot⁡70∘=tan⁡20∘cot⁡(90∘−20∘)\therefore\frac{\tan 20^{\circ}}{\cot 70^{\circ}} = \frac{\tan 20^{\circ}}{\cot\left( 90^{\circ} - 20^{\circ} \right)}
=tan20∘tan20∘=1= \frac{tan20^{\circ}}{tan20^{\circ}} = 1

Source: Grass-G / M-18 Mathematics Paper 27 Nov Third.docx

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