Question

Write 3 equivalent expressions for cot^2x + 1

Answer 1

`1)\\cosec^2x\\2)\\(1)/(sin^2x) \\3)\\(1)/(1-cos^2x)`

Explanation:

Given :

`cot ^2x+1\\`

Now,

1)

`cot^2x+1\\(cos^2x)/(sin^2x) +(sin^2x)/(sin^2x) \\(cos^2x+sin^2x)/(sin^2x) \\(1)/(sin^2x) \\csc^2x`

2)

`(1)/(sin^2x) =1+cot^2x`

3)

`(1)/(1-cos^2x) =1+cot^2x`