Question

7sin2a+3cos2a =4 then show the tana=1/√3

Answer 1

➡ 7 sin²A + 3 cos²A = 4

➡ 4 sin²A + 3 sin²A + 3 cos²A = 4

➡ 3 sin²A + 3 cos²A = 4 - 4 sin²A

➡ 3( sin²A + cos²A ) = 4( 1 - sin²A )

➡ 3( 1 ) = 4( cos²A )

➡ 3 = 4 × cos²A

$= > \frac{3}{4 } = cos {}^{2} A \\ \\ \\ = > \frac{ \sqrt{3} }{2} = cosA \\ \\ \\ = > cos \: 30 = cosA \\ \\ \\ = > 30 = A$

Hence,

tanA = tan30°

$tanA =\dfrac{1}{ \sqrt{3} }$

Hence, proved.

Answer 2

Don't consider my handwriting

Answer is in below