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Verified Answer :

c)1 + 2cot^2x + 2cscx cotx

because cosc^2x=1+cot^2x

Answer:

Option c - 1+2(cotx)^2+2(coscx)(cotx)[/tex]

Step-by-step explanation:

Given : \((cscx+cotx)^2\)

To find : What is the expression \((cscx+cotx)^2\) the same as?

Solution :

Step 1- Write the expression

\((cscx+cotx)^2\)

Step 2- Solve by using identity \((a+b)^2=a^2+b^2+2ab\)

\((cscx+cotx)^2=(cscx)^2+(cotx)^2+2(coscx)(cotx)\)

Step 3- Using trigonometric identity \(csc^2\theta=1+cot^2\theta\)

\((cscx+cotx)^2=1+(cotx)^2+(cotx)^2+2(coscx)(cotx)\)

\((cscx+cotx)^2=1+2(cotx)^2+2(coscx)(cotx)\)

Option c is same as our solution.

Therefore, Option c is correct.


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