Question

Trig identity simplification

Answer 1

\[\frac{ \tan(\pi/2-x)secx }{ 1-\csc^2x }\]

Answer 2

@jim_thompson5910 @dan815

Answer 3

@TheSmartOne

Answer 4

The numerator if i'm not mistaken, is just sin

Answer 5

Then the denominator I think is -cos^2

Answer 6

Then not sure what to doo..

Answer 7

@radar

Answer 8

\[\tan\left(\frac{\pi}{2}-x\right)=\cot x\]
\[\csc^2x=1+\cot^2x~~\implies~~1-\csc^2x=-\cot^2x\]

Answer 9

Ooh, typo, -cot^2

Answer 10

then what?

Answer 11

Simplify. A factor of \(\cot x\) can be eliminated. Given that \(\sec x=\dfrac{1}{\cos x}\), there might be some more simplification.

Answer 12

Does the numerator not equal sin?

Answer 13

There is, yes, but you can incorporate it into a factor of \(\tan x\).
\[\frac{\tan\left(\frac{\pi}{2}-x\right)\sec x}{1-\csc^2x}=-\frac{\cot x\sec x}{\cot^2x}=-\frac{\sec x}{\cot x}\]
which I suppose you can leave as \(-\sec x\tan x\).

Answer 14

can't be further simplified?

Answer 15

Not that I can see. Mathematica gives the same result.

Answer 16

Alright, got it. Thank you.

Answer 17

yw