Step 1: Analyze the denominator The given integral has the denominator: \[ \sqrt{\cos^4 x - \sin^4 x}. \] Using trigonometric identities, \[ \cos^4 x - \sin^4 x = (\cos^2 x - \sin^2 x)(\cos^2 x + \sin^2 x) = \cos 2x. \]
Step 2: Domain restrictions The function is undefined where the denominator is zero: \[ \cos 2x = 0 \Rightarrow 2x = \frac{\pi}{2} + n\pi. \] Solving for \( x \), \[ x = \frac{\pi}{4} + n\frac{\pi}{2}. \] Thus, the domain of \( f(x) \) is: \[ [(4n - 1) \frac{\pi}{4}, (4n+1) \frac{\pi}{4}]. \]
\[ \text{The domain of the real-valued function } f(x) = \sin^{-1} \left( \log_2 \left( \frac{x^2}{2} \right) \right) \text{ is} \]
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?