Question

If root 3 tan theta minus 1 is equal to zero find the value of sin square theta minus cos square theta

Answer 1

$\sqrt{3} \tan(x) - 1 = 0$

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

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

we know that tan(30°) = 1/√3

Therefore, x = 30°

We have to find sin²(x) - cos²(x)

= sin²(30°) - cos²(30°)

$= { (\frac{1}{2}) }^{2} - {( \frac{ \sqrt{3} }{2}) }^{2}$

$= \frac{1}{4} - \frac{3}{4}$

$= - \frac{ 2}{4}$

$= - \frac{1}{2}$

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Answer 2

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