1.

The value at(tan1° tan2° tan3°..........tan89°)is

Answer»

Tan1° × tan2° × tan3° ×........× tan44° × tan45° × tan46°....... × tan87° × tan88° × tan89°

= tan1° × tan2° × tan3° ×........× tan44° × tan45° × TAN(90-44)°....... × tan(90-3)° × tan(90-2)° × tan(90-1

= tan1° × tan2° × tan3° ×........× tan44° × tan45° × cot44°....... × cot3° × cot2° × cot1°

= (tan1° × cot1°) × (tan2° × cot2°) × (tan3° × cot3°)........× (tan44° × cot44°) × tan45°

= 1 × 1 × 1 × ....... × 1 × 1
= 1



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