The value of tan1° × tan2° × tan3° ×……× tan 89° is , The value of tan1° × tan2° × tan3° ×……× tan 89° is

A. ½

B. 2

C. 1

D. 0

Correct Answer :

C. 1

Explanation

tanθcotθ=1,

tan (90−θ) =cotθ

and tan45°=1

Given: tan1°.tan2°,tan3° …….tan88°. tan89°

= (tan1°. tan89°),(tan2°. tan88°)…..(tan44°.tan46°) (tan45°)

= [(tan1°. tan (90°−1°)]. [(tan 2°. tan(90°−2°)]………. [(tan44°. tan(90°−44°)].1

= (tan1°. cot1°). (tan2°. cot2°) ……. (tan44°. cot44°)

= 1