If `xsin45^@cos^2 60^@=(tan^2 60^@cos e c 30^@)/(s e c 45^@cot^2 30^@),\ t h e n\ x=` `2` b. `4` c. `8` d. `16`

Explanation

We have:



`x sin 45^{circ} cos ^{2} 60^{circ}=frac{tan ^{2} 60^{circ} {cosec} 30^{circ}}{sec 45^{circ} cot ^{2} 30^{circ}} `

`Rightarrow x times(frac{1}{sqrt{2}}) times(frac{1}{2})^{2}=frac{(sqrt{3})^{2} times(2)}{(sqrt{2}) times(sqrt{3})^{2}}`

`Rightarrow frac{x}{4 sqrt{2}}=frac{6}{3 sqrt{2}}`

`Rightarrow x=frac{6}{3 sqrt{2}} times 4 sqrt{2}`

`Rightarrow x=8`
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