Part CCSIR NET December 2025mixing-a-holomorphic-term-with-cos-squared-of-the-modulus-breaks-holomorphy-almost-everywhere-check-a-non-real-point-directly

Mixing a holomorphic term with cos squared of the modulus breaks holomorphy almost everywhere check a non real point directly

Let $f:\mathbb{C}\to\mathbb{C}$ be defined by $f(z)=\sin^{2}z+\cos^{2}$ |z|. Which of the following statements are true?

A.f is a real valued function.
B.f(z) = 1 for all $z\in\mathbb{C}$ .
C.f is not an entire function.✓
D.f has finitely many zeros on the imaginary axis.✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Mixing a holomorphic term with cos squared of the modulus breaks holomorphy almost everywhere check a non real point directly

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