The value of tan $1^{o}$ tan $2^{o}$ tan $3^{o}$ .... tan $89^{o}$ is.

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $1$
We have to find the value of $t a n 1^{0} t a n 2^{0} t a n 3^{0} . . . . . t a n 89^{0}$
We know that $t a n 89^{0} = t a n (90^{0} - 1^{0}) = c o t 1^{0}$
Similarly $t a n 88^{0} = c o t 2^{0}$ and so on
Finally we have $t a n 46^{0} = c o t 44^{0}$
So we get $t a n 1^{0} t a n 2^{0} . . . . . . . . t a n 89^{0} = (t a n 1^{0} c o t 1^{0}) (t a n 2^{0} c o t 2^{0}) . . . . . . . . . (t a n 44^{0} c o t 44^{0}) (t a n 45^{0})$
$= (1) (1) . . . . . (1) (1) = 1$

Suggest Corrections

Similar questions

tan x - {tan}^{2} x = 1

{tan}^{4} x - 2 {tan}^{3} x - {tan}^{2} x + 2 tan x + 1

tan 1^{0} tan 2^{0} tan 3^{0} . . . . tan 89^{0}

tan 1^{0} tan 2^{0} tan 3^{0} . . . . . . . tan 89^{0}

{tan}^{- 1} (tan 1) + {tan}^{- 1} (tan 2) + {tan}^{- 1} (tan 3) + {tan}^{- 1} (tan 4)

1^{\circ}

2^{\circ}

3^{\circ}

\times . . . . . . . . . . \times

89^{\circ}

Join BYJU'S Learning Program