Question

if root 3 tan theta=1, then find the value of sin2theta-cos2theta

Answer 1

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Answer 2

Given that,

The value of $\sqrt{3} \tan\theta=1$

To find,

The value of $\sin^2\theta-\cos^2\theta$

Solution,

We have,

$\sqrt{3} \tan\theta=1$

It means,

$\tan\theta=\dfrac{1}{\sqrt 3}$

We know that, $\tan30=\dfrac{1}{\sqrt 3}$

So,

$\tan\theta=\tan(30)$

i.e. $\theta=30^{\circ}$

Now, put $\theta=30^{\circ}$ in the below equation:

$\sin^2\theta-\cos^2\theta\\\\\sin^2\theta-\cos^2\theta=\sin^2(30)-\cos^2(30)\\\\=(\dfrac{1}{2})^2-(\dfrac{\sqrt3}{2})^2\\\\=\dfrac{1}{4}-\dfrac{3}{4}\\\\=\dfrac{-1}{2}$

So, the value of $\sin^2\theta-\cos^2\theta$ is $\dfrac{-1}{2}$.