Question

please tell me answer.​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

Step-by-step explanation:

GIVEN:

$\sqrt{3}tan\theta=3 sin\theta$

TO FIND:

$sin^{2}\theta - cos^{2}\theta$

ANSWER:

=>$\sqrt{3}tan\theta=3 sin\theta$

=>$\sqrt{3}\dfrac{sin\theta}{cos\theta}=3sin\theta$

On eliminating $sin\theta<strong> </strong>$ both sides,

=>$\dfrac{1}{cos\theta}=\sqrt{3}$

=>$cos\theta= \dfrac{1}{\sqrt{3}}$

So,

$cos^{2}\theta=\dfrac{1}{3}$

And we know,

$\large\red{\boxed{ sin^{2}\theta - cos^{2}\theta = 2cos^{2}\theta - 1}}$

= $2cos^{2}\theta - 1$

= $\dfrac{2× 1}{3} - 1$

=$\dfrac{2}{3}-1$

=$\dfrac{2-3}{3}$

=$\dfrac{-1}{3}$

$\huge\green{\boxed{ ANSWER=\dfrac{-1}{3}}}$