If \(x\) tan 30° = \(\frac{\text{sin 30° + cos 60°}}{\text{tan 60�

1.	If \(x\) tan 30° = \(\frac{\text{sin 30° + cos 60°}}{\text{tan 60° + sin 60°}}\), then the value of \(x\) is :(a) \(\frac23\)(b) \(\frac2{\sqrt3}\)(c) \(\frac2{3\sqrt3}\)(d) \(\frac32\)
Answer» (a) \(\frac23\) \(x\) tan 30° = \(\frac{\text{sin 30° + cos 60°}}{\text{tan 60° + sin 60°}}\) = \(\frac{\frac12+\frac12}{\sqrt3+\frac{\sqrt3}{2}}=\frac{1}{\frac{2\sqrt3+\sqrt3}{2}}=\frac{2}{3\sqrt3}\) \(x\times\frac1{\sqrt3}=\frac{2}{3\sqrt3}\) ⇒ \(x\) = \(\frac{2\sqrt3}{3\sqrt3}=\frac23.\)

If \(x\) tan 30° = \(\frac{\text{sin 30° + cos 60°}}{\text{tan 60° + sin 60°}}\), then the value of \(x\) is :(a) \(\frac23\)(b) \(\frac2{\sqrt3}\)(c) \(\frac2{3\sqrt3}\)(d) \(\frac32\)

Answer»

(a) \(\frac23\)

\(x\) tan 30° = \(\frac{\text{sin 30° + cos 60°}}{\text{tan 60° + sin 60°}}\)

= \(\frac{\frac12+\frac12}{\sqrt3+\frac{\sqrt3}{2}}=\frac{1}{\frac{2\sqrt3+\sqrt3}{2}}=\frac{2}{3\sqrt3}\)

\(x\times\frac1{\sqrt3}=\frac{2}{3\sqrt3}\) ⇒ \(x\) = \(\frac{2\sqrt3}{3\sqrt3}=\frac23.\)