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Introduction to Trigonometry
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16/06/2021 10:46 am
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Write all the other trigonometric ratios of ∠A in terms of sec A.
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16/06/2021 10:47 am
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
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)