Question

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

Answer 1

Explanation:

Recall that

`\sin(-x) = -\sin x`

Therefore,

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

so

`\csc(-x)\tan x = \left(-(1)/(\sin x)\right)\left((\sin x)/(\cos x)\right)`

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