Question

Verify the identity algebraically: Csc(-x)tanx =-secx

Answer 1

Step-by-step explanation:

Recall that

$\sin(-x) = -\sin x$

Therefore,

$\csc(-x) = \dfrac{1}{\sin(-x)} = -\dfrac{1}{\sin x}$

so

$\csc(-x)\tan x = \left(-\dfrac{1}{\sin x}\right)\left(\dfrac{\sin x}{\cos x}\right)$

$\:\:\:\:\:\:\:\:\:= -\dfrac{1}{\cos x} = -\sec x$