Question

( EXERCISE 84
1. Express the trigonometric ratios sin A, sec A and tan Ain terms of cot A​

Answer 1

Answer:

1+cot² A =cosec²

Step-by-step explanation:

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Answer 2

Answer :-

Cosec^2A = 1 + Cot^2 A

1/ Cosec^2 A = 1/1 + Cot^2 A

We know that ,

Sin^2 A = 1 / 1 + Cot^2

Sin A = ± 1 / √ 1 + Cot^2 A

Therefore,

Sin A = 1 / √ 1 + Cot^2A

We know that ,

Tan A = Sin A / Cos A

However ,

Cot A = Cos A / Sin A

Therefore,

Tan A = 1 / Cot A

Also ,

Sec^2 A = 1 + Tan^2 A

= 1 + 1 / Cot^2 A

= Cot^2 + 1 / Cot^2 A

Therefore,

Sec A = √ Cot^2A + 1 / Cot A