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2. Write all the other trigonometric ratios of ∠A in terms of sec A.

2. Write all the other trigonometric ratios of ∠A in terms of sec A.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
4 months ago
Cos A function in terms of sec A: sec A = 1/cos A ⇒ cos A = 1/sec A sec A function in terms of sec A: cos2A + sin2A = 1 Rearrange the terms sin2A = 1 – cos2A sin2A = 1 – (1/sec2A) sin2A = (sec2A-1)/sec2A sin A = ± √(sec2A-1)/sec A cosec A function in terms of sec A: sin A = 1/cosec A ⇒cosec A = 1/sin A cosec A = ± sec A/√(sec2A-1) Now, tan A function in terms of sec A: sec2A – tan2A = 1 Rearrange the terms ⇒ tan2A = sec2A – 1 tan A = √(sec2A – 1) cot A function in terms of sec A: tan A = 1/cot A ⇒ cot A = 1/tan A cot A = ±1/√(sec2A – 1)

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