IAT (IISER) 2026 | Trigonometric Ratios & Identities Question 1 | Mathematics

Consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \sin^2(7x) - \sin^2(5x)$. Which of the following statements is NOT TRUE?

$f$ is increasing on $\left(\dfrac{3\pi}{2}, 2\pi\right)$.

$f(x) > 0$, for all $x \in \left(0, \dfrac{\pi}{48}\right)$.

$f\left(x + \dfrac{\pi}{2}\right) + f(x) = 0$, for all $x \in \mathbb{R}$.

$f\left(\dfrac{\pi}{12}\right) = 0$

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