Question

The value of (tan1° tan2° tan3° ... tan89°)is.... any one help me with full explanation?
answer=1

Answer 1

Hello friend..

◆ using complementry angle formula .

=) tan(90 -@) = cot@

according to question.

=) tan1°tan2°tan3°.......tan89°

there are 89 terms in which one term is tan45° which is equal to 1

so remaining left 88 terms .

we can write all terms as :-

=) tan 89° = tan(90 -1) = cot1°

=) tan88° = tab(90-2) = cot2°

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..

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=) tan44° = tan(90-44) = cot44°

now using above we can write.,

=) tan1°tan2°tan3°.......cot3°cot2°cot1°

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

so we know that :-

◆tanA×cotA = 1

then, above expression is equal to

=) tan1°cot° = 1

similarly

=) tan2°cot2° = 1

.
.

. .
...
=) tan44°cot44° =1

all values are equal to 1.

=) tan1°tan2° ..........tan89° = 1

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hope it will. help u

Answer 2

Tan1°tan2°.....tan89°
tan1°tan(90-1)°......Tan(90_89)°
Tan1cot1=1