Question

Express trigonometric ratio sec A in terms of cot A.​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:\sec\:A\:=\:\dfrac{\sqrt{\cot^2\:A\:+\:1}}{\cot\:A}}}}$

Step-by-step-explanation:

We have to express the trigonometric ratio sec A in terms of cot A.

We know that,

$\displaystyle{\pink{\sf\:1\:+\:\tan^2\:A\:=\:\sec^2\:A}}$

$\displaystyle{\implies\sf\:\sec\:A\:=\:\sqrt{\:1\:+\:\tan^2\:A}}$

$\displaystyle{\implies\sf\:\sec\:A\:=\:\sqrt{1\:+\:\left(\:\dfrac{1}{\cot\:A}\:\right)^2}\:\qquad\dots\:\left[\:\tan\:A\:=\:\dfrac{1}{\cot\:A}\:\right]}$

$\displaystyle{\implies\sf\:\sec\:A\:=\:\sqrt{1\:+\:\dfrac{1}{\cot^2\:A}}}$

$\displaystyle{\implies\sf\:\sec\:A\:=\:\sqrt{\dfrac{\cot^2\:A\:+\:1}{\cot^2\:A}}}$

$\displaystyle{\implies\sf\:\sec\:A\:=\:\dfrac{\sqrt{\cot^2\:A\:+\:1}}{\sqrt{\cot^2\:A}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:\sec\:A\:=\:\dfrac{\sqrt{\cot^2\:A\:+\:1}}{\cot\:A}}}}}$

Answer 2

Answer:

• We have to express the trigonometric ratio sec A in the terms of cot A..

We know that,

• 1 + tan2 A = sec2 A

=> sec A = √ 1 + tan2

=> sec A = √ 1 + ( 1 / cot A)2

=> sec A = √ 1 + 1 / cot2 A

=> sec A = √ cot2 A+1 / √ cot2 A

=> sec A = √ cot2 A+1 / cot A