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

Mathematics

1 answer:

weqwewe [10]2 years ago

5 0

Step-by-step explanation:

Recall that

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

Therefore,

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

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

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

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