Question

If tan A + 1/tan A = 2 , then the value of cosec A is​

Answer 1

Given:

$\begin{gathered}\sf tanA+\frac{1}{tanA}=2\\\end{gathered}$

To find: The value of Cosec A will be ?

Solution:

Step 1: Take LCM

$\begin{gathered}\sf\frac{tan^2A+1}{tanA}=2\\\end{gathered}$

Step 2: Cross multiply tan A

$\begin{gathered}\sf {tan^2A+1}=2tanA\\\end{gathered}$

or

$\begin{gathered}\sf tan^2A-2tanA+1=0\\\end{gathered}$

it's a quadratic equation in tanA, it can be converted to complete square term.

$\begin{gathered}\sf ( {x + y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ \end{gathered}$

Thus,

$\begin{gathered}\sf (tanA-1)^2=0\\\end{gathered}$

or

$\begin{gathered}\sf (tanA-1)=0\\\end{gathered}$

Step 3: find value of A

as tan 45°=1

So,

$\begin{gathered}\sf tanA=tan 45°\\\end{gathered}$

cancel tan from both sides

A=45°

Step 4: Find the value of cosec A

cosec 45°=√2

Final answer:

If tanA + 1/tanA =2, then the value of Cosec A will be √2.

Answer 2

Answer:

Step-by-step explanation: