Question

The value of tan 40 tan 50 tan 60 is?

Answer 1

Step-by-step explanation:

tan40.tan50.tan60

= (1/cot40)tan50.tan60

= (1/tan(90-40).tan50.tan60

= (1/tan50).tan50. tan60

= 1.tan60

=tan60

= √3

Answer 2

The value of $\tan40.\tan50.\tan60=\sqrt{3}$

Step-by-step explanation:

We have,

$\tan40.\tan50.\tan60$

To find, the value of $\tan40.\tan50.\tan60=?$

∴ $\tan40.\tan50.\tan60$

= $\tan40.\tan (90-40).\tan60$

$=\tan40.\cot 40.\tan60$

Using trigonometric identity,

$\tan (90-A)=\cot A$

$=\tan40.\dfrac{1}{\tan 40} .\tan60$

Using trigonometric identity,

$\cot A=\dfrac{1}{\tan A}$

$=1.\sqrt{3}$

[ ∵ $\tan60=\sqrt{3}$]

$=\sqrt{3}$

Hence, the value of $\tan40.\tan50.\tan60=\sqrt{3}$