Answer:
True
Step-by-step explanation:
Given: [tex]\csc^2x-1=\cot^2x[/tex]
To find: False or True
Taking left side of equation
[tex]\Rightarrow \csc^2x-1[/tex]
[tex]\Rightarrow \dfrac{1}{\sin^2}-1[/tex] [tex]\because \csc x=\dfrac{1}{\sin x}[/tex]
[tex]\Rightarrow \dfrac{1-\sin^2x}{\sin^2}[/tex]
[tex]\Rightarrow \dfrac{\cos^2x}{\sin^2}[/tex] [tex]\because 1-\sin^2x=\cos^2[/tex]
[tex]\Rightarrow \cot^2x[/tex]
Thus, The left hand side is equal to right ahnd side.
Hence, The statement is true.
