Question

If tan∅ = 1/√3 then
Find sin²∅ - cos²∅​

Answer 1

Answer:

the angle will be 30°

so ,

sin^2 - cos ^2 will be (1-√3)/2

Answer 2

$tan \: \alpha = \frac{1}{ \sqrt{3} } \\ \\ given \: is \\ \\ {sin}^{2} \alpha - {cos}^{2} \alpha \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ................(1) \\ \\ eqution(1) \: is \: devide \: by \: {cos}^{2} \alpha \\ \\ = \frac{ {sin}^{2} \alpha - {cos}^{2} }{ {cos}^{2} \alpha } \\ \\ = \frac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha } - \frac{ {cos}^{2} \alpha }{ {cos}^{2} \alpha } \\ \\ = {tan}^{2} \alpha - 1 \\ \\ = ( \frac{1}{ \sqrt{3} } ) ^{2} - 1 \\ \\ = \frac{1}{3} - 1 \\ \\ = \frac{1 - 3}{3} \\ \\ = \frac{ - 2}{3}$

Hope it helps....

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