Final answer:
The Pythagorean identities can indeed be used in expanding (1−2sin²x)², following standard algebraic rules for binomial squares, leading to the expansion 1−4sin²x+4sin´x.
Step-by-step explanation:
Yes, you can still use Pythagorean identities in expanding the expression (1−2sin²x)². By squaring the expression, you follow basic algebraic rules of expansion (binomial squaring). The expression becomes:
(1−2sin²x)(1−2sin²x) = 1 - 2sin²x - 2sin²x + 4sin´x = 1−4sin²x+4sin´x
This result corresponds to answer choice 'a'. You are basically using the algebraic identity (a-b)² = a² - 2ab + b², where 'a' is 1 and 'b' is 2sin²x in this case.