Question

express sec theta in terms of cot theta

Answer 1

sec theta in terms of cot theta 
 we know that ,
sec²β-tan²β=1
⇒sec²β=1+tan²β
⇒sec²β=1+1/cot²β
⇒secβ=root over (1+(1/cot²β))

Answer 2

Answer:

$sec\theta =\frac{\sqrt{(cot^{2}\theta+1)}}{cot\theta}$

Explanation:

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We know the Trigonometric identity:

Sec²A = 1+tan²A

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Now ,

$sec\theta$

= $\sqrt{1+tan^{2}\theta}$

= $\sqrt{1+\frac{1}{cot^{2}\theta}}$

=$\sqrt{\frac{(cot^{2}\theta+1)}{cot^{2}\theta}}$

= $\frac{\sqrt{(cot^{2}\theta+1)}}{cot\theta}$

Therefore,

$sec\theta =\frac{\sqrt{(cot^{2}\theta+1)}}{cot\theta}$

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