Question

What basic trigonometric identity would you use to verify that cscx secx cotx=csc^2x

Answer 1

We are given an trigonometry expression and to prove it using trigonometry identity.

`\csc x \sec x\cot x=\csc^2x`

Trigonometry Identity,

`\sec x=(1)/(\cos x)`

`\cot x=(\cos x)/(\sin x)`

`\csc x=(1)/(\sin x)`

Taking Left hand side,

`\Rightarrow\csc x\cdot\sec x\cdot \cot x`

`\Rightarrow\csc x\cdot(1)/(\cos x)\cdot(\cos x)/(\sin x)`

Cancel like terms from numerator and denominator

`\Rightarrow\csc x\cdot(1)/(\sin x)`

`\Rightarrow\csc x\cdot\csc x`

`\Rightarrow\csc^2x=RHS`

Hence Proved