The value of tan 1° tan 2° tan 3° ...... tan 89° is
(a) 1
(b) −1
(c) 0
(d) None of these

Open in App

Solution

Here we have to find:
$tan 1° tan 2° tan 3° ...... tan 89°$
$= t a n (90 - 89) ° t a n (90 - 88) ° t a n (90 - 87) ° . . . . . . t a n 89 °$
$= c o t 89 ° c o t 88 ° c o t 87 ° . . . . . . t a n 89 °$
$= c o t 89 ° t a n 89 ° c o t 88 ° t a n 88 ° c o t 87 ° t a n 87 ° . . . . . . t a n 45 °$
$= 1 \times 1 \times 1 \times . . . . . .1$
$= 1$
Hence the correct option is1

Suggest Corrections

Similar questions

Q. tan 1° tan 2° tan 3° ... tan 89° = ?
(a) 1
(b) 0
(c) Cannot be determined
(d) None of these

Q. The value of

\tan 1 ° \tan 2 ° \tan 3 ° . . . \tan 89 °

is

(a) 0 (b) 1 (c)

\frac{1}{2}

(d) not defined

Question 6
The value of $(t a n 1^{\circ}, t a n 2^{\circ}, t a n 3^{\circ} \dots \dots t a n 89^{\circ})$ is

(A) 0
(B) 1
(C) 2
(D) $\frac{1}{2}$

Q. Find the value

t a n 1^{\circ} . t a n 2^{\circ} . t a n 3^{\circ} . . . . . . . . . . t a n 89^{\circ}

Q. The value of

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . . . tan 89^{\circ}

Join BYJU'S Learning Program

The value of tan 1° tan 2° tan 3° ...... tan 89° is(a) 1(b) −1(c) 0(d) None of these

Here we have to find: tan 1° tan 2° tan 3° ...... tan 89° =tan(90−89)°tan(90−88)°tan(90−87)°......tan89°=cot89°cot88°cot87°......tan89°=cot89°tan89°cot88°tan88°cot87°tan87°......tan45°=1×1×1×......1=1Hence the correct option is1

The value of tan 1° tan 2° tan 3° ...... tan 89° is
(a) 1
(b) −1
(c) 0
(d) None of these