1/2-sin^2A +1/2+tan^2A =1 prove it
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at least attach a picture or something. question is not clear
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We have to prove (1-tan^2 a) /(1+tan^2 a)= 2 cos^2 a - 1.
(1-tan^2 a) /(1+tan^2 a)= 2 cos^2 a - 1
LHS = (1-tan^2 a) /(1+tan^2 a), or
= [(cos^2 a - sin^2 a)/cos^2 a]/[(cos^2 a + sin^2 a)/cos^2 a], or
= [(cos^2 a - sin^2 a)/cos^2 a]*cos^2 a/(cos^2 a + sin^2 a), or
( Here cos^2 a get cancelled, and cos^2 a + sin^2 a = 1), or
= cos^2 a - sin^2 a [ Here sin^2 a = 1 - cos^2 a], or
= cos^2 a - 1 +cos^2 a
= 2cos^2 a - 1 = RHS. Proved.
(1-tan^2 a) /(1+tan^2 a)= 2 cos^2 a - 1
LHS = (1-tan^2 a) /(1+tan^2 a), or
= [(cos^2 a - sin^2 a)/cos^2 a]/[(cos^2 a + sin^2 a)/cos^2 a], or
= [(cos^2 a - sin^2 a)/cos^2 a]*cos^2 a/(cos^2 a + sin^2 a), or
( Here cos^2 a get cancelled, and cos^2 a + sin^2 a = 1), or
= cos^2 a - sin^2 a [ Here sin^2 a = 1 - cos^2 a], or
= cos^2 a - 1 +cos^2 a
= 2cos^2 a - 1 = RHS. Proved.
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