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Trigonometric Ratios and Identities
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In trigonometry, fundamental identities are used for simplification of expressions having trigonometric ratios.

Example: Prove that
cot + tan = cosec sec .


Example: Show that
tan4A + tan2A = sec4A - sec2A.

= tan4A + tan2A
= tan2 A (tan2A + 1)
= (sec2A - 1) (sec2A) [Using Identity: 1 + tan2 = sec2]
= sec4A - sec2A = RHS
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