Prove that 1 - tan ^2 A/1 + tan^2A = 1 - 2sin^2 A
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Explanation:
L.H.S = 1−tan2a1+tan2a=1−sin2acos2a1+sin2acos2a
=cos2a−sin2acos2acos2a+sin2acos2a
=cos2a−sin2acos2a+sin2a
=cos(2a)1=cos2a , since cos2a=cos2a−sin2aandcos2a+sin2a=1
∴ L.H.S=R.H.S
L.H.S = 1−tan2a1+tan2a=1−sin2acos2a1+sin2acos2a
=cos2a−sin2acos2acos2a+sin2acos2a
=cos2a−sin2acos2a+sin2a
=cos(2a)1=cos2a , since cos2a=cos2a−sin2aandcos2a+sin2a=1
∴ L.H.S=R.H.S
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