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

Asked by Abhisek | 1 year ago |  62

1 Answer

Solution :-

Cos A function in terms of sec A:

sec A = \( \dfrac{1}{cos A}\)

⇒ cos A = \( \dfrac{1}{sec A}\)

sec A function in terms of sec A:

cos2A + sin2A = 1

Rearrange the terms

sin2A = 1 – cos2A

sin2A = 1 – (\( \dfrac{1}{sec^2 A} \))

sin2A = \( \dfrac{(sec^2A-1)}{sec^2A}\)

sin A = ± \( \dfrac{\sqrt{(sec^{2}A-1}}{sec A}\)

cosec A function in terms of sec A:

sin A = \( \dfrac{1}{cosec A}\)

⇒cosec A = \( \dfrac{1}{sin A}\)

cosec A = ± \( \dfrac{sec A}{\sqrt{sec^2A-1}}\)

Now, tan A function in terms of sec A:

sec2A – tan2A = 1

Rearrange the terms

⇒ tan2A = sec2A – 1

tan A = \(( {\sqrt{sec^2A-1}})\)

cot A function in terms of sec A:

tan A = \( \dfrac{1}{cotA}\)

⇒ cot A = \( \dfrac{1}{tanA}\)

cot A = \( \dfrac{±1}{( {\sqrt{sec^2A-1}})}\)

Answered by Pragya Singh | 1 year ago

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Evalute the following:

(i) \( \dfrac{sin 20°}{ cos 70°}\)

(ii) \(\dfrac{ cos 19°}{ sin 71°}\)

(iii) \( \dfrac{sin 21°}{ cos 69°}\)

(iv) \( \dfrac{tan 10°}{ cot 80°}\)

(v) \( \dfrac{sec 11°}{ cosec 79°}\)

Class 10 Maths Introduction to Trigonometry View Answer