Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Put $a=\sqrt{3}\sin x+\cos x=2\sin (x+\pi /6)$. The exponent is $\sqrt{a^2}=|a|$. At A and $\mathrm{D},a=2$ and -2 respectively, with exponent 2; each yields 4. At B and C the expression does not equal 4. A negative base raised to a noninteger exponent is undefined over the reals; the qualifying D has integer exponent 2.