Question

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

Answer 1

The basic identities that will be used is:

cscx = 1/sinx
secx = 1/cosx
cotx = cosx/sinx

cscx * secx = 1/sinxcosx

cscx * secx* cotx = 1/(sinxcosx)  * cosx/sinx = 1/sin^2x = csc^2x

Answer 2

Solution:

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

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

Trigonometry Identity,

$\sec x=\frac{1}{\cos x}$

$\cot x=\frac{\cos x}{\sin x}$

$\csc x=\frac{1}{\sin x}$

Taking Left hand side,

$\Rightarrow\csc x\cdot\sec x\cdot \cot x$

$\Rightarrow\csc x\cdot\frac{1}{\cos x}\cdot\frac{\cos x}{\sin x}$

Cancel like terms from numerator and denominator

$\Rightarrow\csc x\cdot\frac{1}{\sin x}$

$\Rightarrow\csc x\cdot\csc x$

$\Rightarrow\csc^2x=RHS$

Hence Proved