If cos4 theta minus sin4 theta 23 then the value of 1 minus 2sin2 theta is ........

Quantitative Aptitude ( CCS) Trignometry

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If cos⁴θ−sin⁴θ=23, then the value of 1−2sin²θ is,

3/2

2/3

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Explanation:

Using basic algebraic relation of a²−b²=(a+b)(a−b), we transfom the given equation to,
cos⁴θ−sin⁴θ=2/3
Or, (cos²θ+sin²θ)(cos²θ−sin²θ)=2/3
Or, (cos²θ−sin²θ)=2/3.
Or, 1−sin²θ−sin²θ=2/3,
Or, 1−2sin²θ=2/3.
RHS remained unchanged and only LHS needed transformation.