Question

tan73+cot61/tan17+cot29

Answer 1

Tan 73°+cot 61°/tan 17°+cot 29°
= 1+1/cot 73°×tan 17°+tan 61°×cot 29°
= 2/1+1
= 2/2
= 1 //Ans

Answer 2

$\dfrac{\tan73+\cot61}{\tan17+\cot29}=\tan 73.\cot 61$

Step-by-step explanation:

We have,

$\dfrac{\tan73+\cot61}{\tan17+\cot29}$

To find,$\dfrac{\tan73+\cot61}{\tan17+\cot29}=?$

∴ $\dfrac{\tan73+\cot61}{\tan17+\cot29}$

$=\dfrac{\tan73+\cot61}{\tan(90-73)+\cot (90-61)}$

$=\dfrac{\tan73+\cot61}{\cot 73+\tan 61}$

$=\dfrac{\tan73+\cot61}{\dfrac{1}{\tan 73} +\dfrac{1}{\cot 61}}$

$=\dfrac{\tan73+\cot61}{\dfrac{\tan73+\cot61}{\tan 73.\cot 61}}$

$=\tan 73.\cot 61$

Hence, $\dfrac{\tan73+\cot61}{\tan17+\cot29}=\tan 73.\cot 61$