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1+cos2A/cos2A = tan2A/tanA prove LHS=RHS

1+cos2A/cos2A = tan2A/tanA prove LHS=RHS
asked 70.5k views
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1+cos2A/cos2A = tan2A/tanA prove LHS=RHS

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User Mayur Patel
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1 Answer

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RTP: (1 + cos(2A))/(cos(2A)) = (tan(2A))/(tan(A))


LHS = (1 + cos(2A))/(cos(2A))

= (1 + (1 - tan^(2)(A))/(1 + tan^(2)(A)))/((1 - tan^(2)(A))/(1 + tan^(2)(A)))

= ((1 + tan^(2)(A) + 1 - tan^(2)(A))/(1 + tan^(2)(A)))/((1 - tan^(2)(A))/(1 + tan^(2)(A)))

= (2)/(1 - tan^(2)(A))

= (2)/(1 - tan^(2)(A)) \cdot (tan(A))/(tan(A))

= ((2tan(A))/(1 - tan^(2)(A)))/(tan(A))

= (tan(2A))/(tan(A))

= RHS, as required.
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User JFBM
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