Question 153

The value of tan1°tan2°tan3° ……………tan89° is

Solution

Expression : tan1°tan2°tan3° ……………tan88°tan89°

$$\because$$ $$tan(90^{\circ}-\theta) = cot\theta$$

=> tan 89° = tan(90°-1) = cot 1°

Similarly, tan 88° = cot 2° and so on till tan 46° = cot 44°

=> (tan1°tan2°tan3°.......tan45°......cot3°cot2°cot1°)

Using, $$tan\theta cot\theta$$ = 1 and $$tan45^{\circ}$$ = 1

=> 1*1 = 1

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