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

Question

asked Aug 18, 2018 156k views

1 Answer

Anuran Barman · Answer 1 · 2018-08-22T08:47:43+0000

Solution:

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

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

Trigonometry Identity,

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

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

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

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