Question 109

Evaluate: tan 1° tan 2° tan 3° …………….tan 89°

Solution

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tan 1° tan 2° tan 3° …………….tan 88° tan 89°

= tan 1° tan 2° tan 3 ° ...........tan 43° tan 44° tan 45° cot 44° cot 43°..........cot 2° cot 1°

As we know tan 1° X cot 1° = tan 2° X cot 2° = ........................= tan 44° X cot 44° = 1

and tan 45° = 1

hence ,

tan 1° tan 2° tan 3° …………….tan 88°tan 89° = 1


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