Question

The value of tan 1 tan 2 tan88 tan89 is.

Answer 1

tan 1° tan 2° tan 3° … tan 89°

✯= [tan 1° tan 2° … tan 44°] tan 45°[tan (90° – 44°) tan (90° – 43°)… tan (90° – 1°)]

✯= [tan 1° tan 2° … tan 44°] [cot 44° cot 43 cot 1°] × [tan 45°]

✯= [(tan 1°× cot 1°) (tan 2°× cot 2°)__(tan 44°× cot 44°)] × [tan 45°]

✯ tanA × cotA =1 and

tanA × cotA =1 andtan45° = 1

, the equation becomes= 1 × 1 × 1 × 1 × …× 1= .1 {As 1ⁿ = 1}Answer

Hence, the equation becomes= 1 × 1 × 1 × 1 × …× 1= 1 {As 1ⁿ = 1}

Answertan 1° tan 2° tan 3° … tan 89° = 1

Answer 2

Answer:

tan 1 tan2 ----- tan88 tan89

tan1 tan2-------tan(90-2) tan(90-1)

tan1 tan2------ cot 2 cot1

tan1.cot1=1

tan2.cot2=1

so all cancel each other

answer will be=1