Question

if tan A=1/root 3 then find the value of sin2A

Answer 1

sin2A = 2tanA/1+tan²

given :- tanA = 1/√3

so

sin2A = 2×1√3/1+ (1/√3)²

= 2/√3 ×3/4

= √3/2

## hope it can help you ....♠

Answer 2

Given : The value of tanA is 1/√3

To find : The value of sin2A

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of sin2A)

Here, we will be using general trigonometric identities, in order to calculate the value of sin2A.

So,

= sin2A

= $\frac{2 \tan A }{1 + {\tan }^{2} A}$

$= \frac{2 \times \frac{1}{ \sqrt{3} } }{1 + { (\frac{1}{ \sqrt{3} }) }^{2} }$

$= \frac{ \frac{2}{ \sqrt{3} } }{1 + \frac{1}{3} }$

$= \frac{ \frac{2}{ \sqrt{3} } }{ \frac{3 \times 1 + 1}{3} }$

$= \frac{ \frac{2}{ \sqrt{3} } }{ \frac{4}{3} }$

$= \frac{2}{ \sqrt{3} } \times \frac{3}{4}$

$= \frac{ \sqrt{3} }{2}$

(This value of sin2A will be considered as the final result of this mathematical problem.)

Used formula :

• sin2A = $\frac{2 \tan A }{1 + {\tan }^{2} A}$

Hence, the value of sin2A is $\frac{ \sqrt{3} }{2}$