Question

If root3 tanØ = 3 sinØ , then find the value of sin^2Ø - cos^2Ø​

Answer 1

$\sqrt{3} \tan(x) = 3 \sin(x) \\ \frac{ \sin(x) }{ \cos(x) } = \frac{3}{ \sqrt{3} } \sin(x) \\ \cos(x )= \frac{1}{ \sqrt{3} }$

${ \sin {}^{2} (x) } - { \cos {}^{2} (x) }\\ = 1 - \cos {}^{2} (x ) - \cos {}^{2} (x) \\ = 1 - 2( \frac{1}{ \sqrt{3} } ) {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 1 - \frac{2}{3} = \frac{1}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer 2

Answer:

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