Question

NCERT
Q.2. Write all other T-raitos of angle A in terms of sec A.​

Answer 1

Answer:

Step-by-step explanation:

We know that  

sec^2A−tan^2A=1

⇒tan^2A=sec^2A−1

⇒tan A= √(sec2A−1)  e  q (1)

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We know that  

cos A = 1 ÷ sec A      e q (2)

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We know that  

sin^2A + cos^2A =1

⇒sin^2A = 1 − cos^2A

Putting (2) in the above equation we get

sin2A=1−(1÷ sec A)^2 = (sec^2A−1)÷ sec^2A

⇒sin A= √(sec2A−1) ÷ sec A           e q  (3)

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We know that  

cosec A= 1 ÷ sin A

Putting (3) in the above equation, we get

cosec A = se c A ÷ (√sec^2A−1)     e q (4)

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We know that  

cot A = 1 ÷ tan A

Putting (1) in the above equation, we get

cot A= 1 ÷ (√sec2A−1)           e q (5)

(1), (2), (3), (4) and (5) shows all the other trigonometric ratios of ∠A in terms of sec A.

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