Question

Prove that tan A +cot A = sec A cosec A

Answer 1

tan A +cot A
sinA/cosA +cos A/sin A
on taking LCM
(Sin²A+cos²A)/sinA cos A
As we know sin²A+cos²A=1
1/sinA cosA⇒cosecA secA                          {1/cosA=secA, 1/sinA=cosecA}
Hence proved.........................

Answer 2

Given : The given equation is, tan A +cot A = sec A cosec A

To find : To prove the given equation.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to prove the given equation)

Here, we will be using general trigonometric identities.

Working on LHS,

= tan A + cot A

$= \frac{ \sin(A) }{ \cos(A) } + \frac{ \cos(A) }{ \sin(A) }$

$= \frac{ {sin}^{2}(A) + {cos}^{2}(A ) }{ \cos(A) \sin(A) }$

$= \frac{1}{\cos(A) \sin(A)}$

$= \frac{1}{\cos(A)} \times \frac{1}{\sin(A)}$

$= sec(A) + cosec(A)$

= RHS (proved)

Hence, the given equation (tan A +cot A = sec A cosec A) is proved.