Given trigonometric identity is sec(A+B)=[cos(A-B)]/[cos^2A-sin^2B]

Start from left side

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Substitute formula : cos(A+B) = cosAcosB - sinAsinB \ \

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Rationalize with cosAcosB+sinAsinB

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Substitute formula : sin²A = 1-cos²A and cos²B = 1- sin²B

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Substitute formula : cos(A+B) = cosAcosB-sinAsinB

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Solution :

The Trigonometric identity is sec(A+B)=[cos(A-B)]/[cos^2A-sin^2B] is established