Question

What is the expression (cscx+cotx)^2 the same as?

a)1 + 2csc^2x
b)csc^2x + 2cscx + cot^2x
c)1 + 2cot^2x + 2cscx cotx
d)csc^2x + cot^2x

Answer 1

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

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

Answer 2

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

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.