Question

cos² A - sin² A = 2 cos² A - 1​

Answer 1

Answer:

$wkt \\ {cos}^{2} a + {sin}^{2} a = 1 \\ substitute \: this \: in \: your \: question \\ LHS = \\ {cos}^{2} a - (1 - {cos}^{2} a) = {cos}^{2} a + {cos}^{2} a - 1 \\ = 2 {cos}^{2} a - 1 \\ = RHS \\ hence \: the \: proved$

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Answer 2

Step-by-step explanation:

cos2 a + sin2 a = 1

substitute this in your question

LHS

cos2 a - ( 1 - cos2 a) = cos2 a + cos2 a - 1

= 2 cos2 a - 1

= RHS

HENCE THE PROVE