Question

If √3tan = 3sin , prove that sin2 – cos2 = 1/3.​

Answer 1

√3 Tanx = 3Sinx

Finding Value of Cosx :

√3 Sinx = √3•√3•Sinx

--------

Cosx

1 = √3

--------

Cosx

Cosx = 1

---------

√3

Now Find Value For Sinx

Sin^2 x + Cos^2 x = 1

Sin^2 x = 1 - Cos^2 x

= 1 - ( 1/3) (square of 1/√3 = 1/√3)

Sin^2 x = 2/3

So; Sinx=√(2)

----------

√(3)

NOW FOR ANSWER :

= Sin^2 x - Cos^2 x

= 2 1

------ - ------

3 3

= 1

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3

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