Question

if √3 tanA= 2sinA then find the value of sin^2A-cos^2A​

Answer 1

Step-by-step explanation:

$\sqrt{3} \: tanA = 2 sin A \\ \sqrt{3} \: \: \frac{sin A}{cos A} = 2 sin A \\ \frac{ \sqrt{3} }{cos A} = 2 \\ \frac{ 1}{cos A} = \frac{2}{\sqrt{3} } \\ cos A = \frac{ \sqrt{3} }{2} \\ cos A = cos 30 \degree \\ A = 30 \degree \\ now \\ {sin}^{2} A - {cos}^{2} A \\ = {sin}^{2} 30 \degree - {cos}^{2} 30 \degree \\ = ( \frac{1}{2} )^{2} - ( \frac{ \sqrt{3} }{2} )^{2} \\ = \frac{1}{4} - \frac{3}{4} \\ = \frac{1 - 3}{4} \\ = \frac{ - 2}{4} \\ = - \frac{1}{2}$