Question

Find the value of x...

Answer 1

Answer:

8/3 is the correct answer.

☸Given☸

$\sf{x\sin{60^{\circ}}\cos^{2}{30^{\circ}}=\dfrac{\tan^{2}{45^{\circ}}\sec{60^{\circ}}}{cosec\:60^{\circ}}}$

To Find:

• Value of x

✺Solution✺

We know that,

$\longrightarrow\sf{\sin{60^{\circ}}=\dfrac{\sqrt{3}}{2}}$

$\longrightarrow\sf{\cos{30^{\circ}}=\dfrac{\sqrt{3}}{2}}$

$\longrightarrow\sf{\tan{45^{\circ}}=1}$

$\longrightarrow\sf{\sec{60^{\circ}}=2}$

$\longrightarrow\sf{cosec\:{60^{\circ}}=\dfrac{2}{\sqrt{3}}}$

$\longrightarrow\sf{(\dfrac{\sqrt{3}}{2})^{2}=\dfrac{3}{4}}$

On applying above values in the given equation, we get

$\longrightarrow\sf{x\sin{60^{\circ}}\cos^{2}{30^{\circ}}=\dfrac{\tan^{2}{45^{\circ}}\sec{60^{\circ}}}{cosec\:60^{\circ}}}$

$\longrightarrow\sf{x\times{\dfrac{\sqrt{3}}{2}}\times{( \dfrac{\sqrt{3}}{2})^{2}}=\dfrac{(1)^{2}\times2}{\dfrac{2}{\sqrt{3}}}}$

$\longrightarrow\sf{x\times{\dfrac{\sqrt{3}}{2}}\times{\dfrac{3}{4}}\times{\dfrac{2}{\sqrt{3}}}={1\times2}}$

$\longrightarrow\sf{x\times{\dfrac{3}{4}}=2}$

$\longrightarrow\sf{x=2\times\dfrac{4}{3}}$

$\longrightarrow\sf{\purple{x=\dfrac{8}{3}}}$

Hence, the value of x is $\bf{\green{\dfrac{8}{3}}}$.