The value of ( 70^ )( 10^ 70^ -1) is

Question

The value of $(\sin {70}^{\circ })(\cot {10}^{\circ }\cot {70}^{\circ }-1)$ is

Accepted Answer

$$\cot10^\circ\cot70^\circ - 1 = \frac{\cos10^\circ\cos70^\circ - \sin10^\circ\sin70^\circ}{\sin10^\circ\sin70^\circ} = \frac{\cos80^\circ}{\sin10^\circ\sin70^\circ}$$

$$\sin70^\circ(\cot10^\circ\cot70^\circ-1) = \frac{\cos80^\circ}{\sin10^\circ} = \frac{\sin10^\circ}{\sin10^\circ} = 1$$

(using $\cos80^\circ = \sin10^\circ$).

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