Math, asked by shilpimaiti78, 11 months ago

7. If √3 tan theta = 3 sin theta, prove that (sin’o-cos²0) = 1/3​

Answers

Answered by harendrachoubay
1

(sin^2 \theta-cos^2 \theta)=\dfrac{1}{3}, proved.

Step-by-step explanation:

We have,

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

To prove that, (sin^2 \theta-cos^2 \theta)=\dfrac{1}{3}.

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

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

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

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

\sin \theta=\sqrt{1-\cos^2 \theta}=\sqrt{1-(\dfrac{1}{\sqrt{3}})^2}

\sin \theta}=\sqrt{\dfrac{2}{3}}}

L.H.S. = sin^2 \theta-cos^2 \theta

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

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

= \dfrac{2-1}{3}

= \dfrac{1}{3}

= R.H.S., proved.

Similar questions