If cos2 alpha minus sin2 alpha tan2 beta then the value of cos2 beta minus sin2 beta is ........

Quantitative Aptitude ( CCS) Trignometry

If cos²α−sin²α=tan²β, then the value of cos²β−sin²β is,

cot²β

tan²α

cot²α

tan²β

cos²α−sin²α=tan²β
Or, cos²α−1+cos²α=sec²β−1
Or, sec²β=2cos²α
Or, cos²β=12sec²α.
Or, sin²β=1−12sec²α.
Subtracting,
cos²β−sin²β=sec²α−1=tan²α.

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