Question

prove that
√3tan^2a =3sina .sin^2a-cos^2a​

Answer 1

Hey mate,..

√3 tanA = 3sinA

√3sinA/cosA = 3 sinA

cosA = √3/3

sin² A = 1-cos²A 

 

          = 1-(√3/3)²

   

          = 1- 3/9

 

          =1-1/3

 

         = 2/3

Sin²A-cos²A = 2/3-1/3

 

                    = 1/3

Hope it will help you.

✨ sai.

Answer 2

Answer:

Step-by-step explanation:

From the given data,

√3 tanA = 3sinA

√3 SinA/cosA = 3sinA

Hence cosA= 1/√3

Now,

Sin^2 A + cos^2 A = 1

Therefore sin^2 A= 1- cos^2 A

Sin^2 A= 1- 1/3

Sin^2 A = 2/3

Therefore,

Sin^2 A- cos^2 A = 2/3 - 1/3 = 1/3