Question

Cos thita = sin(90- thita) is a formula. But can we write sin(90- thita) as sin90- sin thita?

Answer 1

No. Let me use "@" instead of "thita". Reason is that if that is true, then 1 - sin@ must equal with cos@ But if we find cos@ in terms of sin@ from pythagorian identity, we get cos @ = ±√(1 - sin² @). Now it's clearly seen that 1 - sin@ ≉ ±√(1 - sin² @). Thus, we can't write so.