Question

7 sin squared theta + 3 cos squared theta equals to 4 so what is the value of tan theta​

Answer 1

Given : 7 sin²A + 3 cos²A = 4

So , 4 sin²A + 3 sin²A + 3 cos²A = 4

=} 4 sin²A + 1 = 4 [Sin²A + Cos²A=1]

=} 4 sin²A = 3

=} sin²A = 3/4

On rooting both sides

sinA = √3/2

Hence , A = 60° [ Sin 60° = √3/2 ]

Hence the value of tanA = tan 60° = √3 [ Tan 60° = √3 ]

Solved.

Answer 2

tan

$7 \sin( \alpha ) {}^{2} + 3 \cos( \alpha ) {}^{2} = 4 \\ 4 \sin( \alpha ) {}^{2} + 3( \sin( \alpha ) {}^{2} + \cos( \alpha ) {}^{2} ) = 4 \\ 4 \sin( \alpha ) {}^{2} + 3 = 4 \\ 4 \sin( \alpha ) {}^{2} = 1 \\ \sin( \alpha {} ) {}^{2} = \frac{1}{4} \\ \sin( \alpha ) = \frac{1}{2} \\ \alpha = \frac{\pi}{6} \\ \tan( \frac{\pi}{6} ) = \frac{1}{ \sqrt{3} }$