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