Question

Help simplifying trigonometric expressions:

Answer 1

\[(1-\sin ^2x)/(sinx-cscx)\]

Answer 2

write csc(x) as 1/sinx. then multiply like binomial by binomial (like we did in quadratics). post and verify!!!

Answer 3

So like this? \[(1-\sin ^2x)/(\sin x-(1/\sin x))\]
Should we convert the 1-sin^2x to cos^2x? Or just continue with
\[(1-\sin^2x)((1/\sin x)-\sin x)\]

Answer 4

out of curiosity, how did you get from
(1−sin2x)/(sinx−(1/sinx))
to
(1−sin2x)((1/sinx)−sinx)
?

Answer 5

Ooh, there was a mistake in multiplying by the reciprocal of the denominator.

Answer 6

How about re-writing
1/(sinx -1/sinx) as sin(x)/ ( sin^2 x - 1) (by multiplying by sinx/sinx)

Answer 7

or even better
-sin(x)/ ( 1-sin^2 x ) by multiplying through by -1/-1

Answer 8

so the expression would simplify to
\[-\sin x\]

Answer 9

that is what I got.

Answer 10

Thank you very much!