Question

If root 3 tan theta = 3 sin theta, find the value of sin'2 theta- cos'2 theta.



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Answer 1

Given,

$\sqrt{3} \: tanΘ = 3 \sinΘ$

Now,

$\sqrt{3} \tanΘ = 0$

$\tanΘ = (0 \div \sqrt{3})$

$\tanΘ = 0$

$Θ = 0 \: degrees$

Again,

$3 \sinΘ = 0$

$\sinΘ = (0 \div 3)$

$\sinΘ = 0$

$Θ = 0 \: degrees$

Therefore,

$\sin^{2}Θ - \cos^{2}Θ = ({0}^{2}) - ({1}^{2})$

$\sin^{2}Θ - \cos^{2}Θ = 0 - 1$

$\sin^{2}Θ - \cos^{2}Θ = - 1$

Hence,

$\sin^{2}Θ - \cos^{2}Θ = - 1$

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