Question

MEDAL - Can someone help?

(cscx - 1)(cscx + 1) = (______)^2

Answer 1

I found that it equals cot^2(x)

Answer 2

@ilfy214 That is correct.

Answer 3

@ilfy214 u have any doubt in trigonometry please convert all other trigonometric ratios in cos or sin. it would be easier to understand

Answer 4

We can verify this through difference of squares and then using the identity \(\bf cot^2(x)+1=csc^2(x)\).

\[\bf (\csc(x)-1)(\csc(x)+1)=\csc^2(x)-1\]Now rearrange identity:\[\bf \cot^2(x)+1=\csc^2(x) \implies \csc^2(x)-1=\cot^2(x)\]

Answer 5

Which then implies that:\[\bf (\csc(x)-1)(\csc(x)+1)=\cot^2(x)\]

Answer 6

so would i just plug in "cos x"

Answer 7

cot*

Answer 8

@ilfy214 The bracket would look like this:\[\bf (\csc(x)-1)(\csc(x)+1)=(\cot(x))^2\]So yes, just plug in cot(x) in the brackets.