Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$E=\frac{1}{\sqrt{b-a}}\cdot \frac{\sqrt{b-a}\sin x}{\sqrt{a+(b-a){\sin }^{2}x}}\sqrt{a+b{\tan }^{2}x}=\frac{\sin x\sqrt{a+b{\tan }^{2}x}}{\sqrt{a{\cos }^{2}x+b{\sin }^{2}x}}=\frac{\sin x}{|\cos x|}$, so (C) is correct. At $x=\frac{11\pi }{4},\frac{\sin x}{|\cos x|}=1$, so (D) is correct.