Solution:
We are given an trigonometry expression and to prove it using trigonometry identity.
[tex] \csc x \sec x\cot x=\csc^2x[/tex]
Trigonometry Identity,
[tex]\sec x=\frac{1}{\cos x}[/tex]
[tex]\cot x=\frac{\cos x}{\sin x}[/tex]
[tex]\csc x=\frac{1}{\sin x}[/tex]
Taking Left hand side,
[tex]\Rightarrow\csc x\cdot\sec x\cdot \cot x[/tex]
[tex]\Rightarrow\csc x\cdot\frac{1}{\cos x}\cdot\frac{\cos x}{\sin x}[/tex]
Cancel like terms from numerator and denominator
[tex]\Rightarrow\csc x\cdot\frac{1}{\sin x}[/tex]
[tex]\Rightarrow\csc x\cdot\csc x[/tex]
[tex]\Rightarrow\csc^2x=RHS[/tex]
Hence Proved
