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Range of Trigonometric Ratios from 0 to 90 Degrees

If √3tan A =3...

Question

If √3 tanA = 3 sinA
Then prove that:- sin²A – cos²A= 1/3

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Solution

√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

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