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What is the least value of tan2 θ + cot2 θ + sin2 θ + cos2 θ + sec2 θ + cosec2 θ?1). 12). 53). 34). 7 |
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Answer» Using these trigonometric identities: sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ cot2 θ + 1 = cosec2 θ Required value: tan2 θ + cot2 θ + sin2 θ + cos2 θ + sec2 θ + cosec2 θ On SIMPLIFYING we get: ⇒ tan2 θ + cot2 θ + 1 + 1 + tan2 θ + 1 + cot2 θ ⇒ 3 + 2(tan2 θ + cot2 θ) Least value of tan2 θ + cot2 θ = 2 ⇒ 3 + 2(2) =7 |
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