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Show that tan4 θ +tan2 θ = sec4 θ -sec2 θ. |
Answer» L.H.S: tan4θ + tan2 θ Taking tan2 θ common, we get tan2 θ (tan2 θ + 1) = tan2 θ sec2 θ [∵ sec2 θ – tan2 θ = 1 ⇒ tan2 θ + 1 = sec2 θ] = (sec2 θ – 1) sec2 θ [∵tan2 θ = sec2 θ – 1] = sec4 θ – sec2 θ : R.H.S |
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