Question

Simplify this expression:
csc(-x) over 1+tan^2 (x)
(Over meaning its a fraction)

Answer 1

Choices are...
tan(x)
-cos(x)tan(x)
-cos(x)cot(x)
sin(x)tan(x)

Answer 2

1+tan^2 x = sec^2 x [ identity] ------(1)

csc (-x) = csc x = 1/sinx -------(2)

sec x = 1/cos x -------(3)

\[\frac{ \csc (-x) }{ 1 + \tan ^{2}x } = \frac{ \csc x }{ \sec ^{2}x}\]
[ from (1) and (3) ]

Answer 3

\[= \frac{ \frac{ 1 }{ \sin x } }{ \frac{ 1 }{ \cos ^{2}x } }\]
[using (2) and (3)
\[= \frac{ \cos ^{2}x }{ sinx }\]

Answer 4

\[=\frac{ \cos x \times cosx }{ \sin x}\]
= cotx cos x