Q)Write the following expression in terms of cosine both in a simplified form?

$\displaystyle \frac{1-csc^2x}{csc^2x} $

- Is my attempt Correct (Wondering))Attempt

$\displaystyle -1(sin^2x-1) =-cos^2x $

Thank you

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- Mar 11th 2009, 10:09 AMmj.alawamiWrite the expressions in terms of cosine?
Q)Write the following expression in terms of cosine both in a simplified form?

$\displaystyle \frac{1-csc^2x}{csc^2x} $

- Is my attempt Correct (Wondering))**Attempt**

$\displaystyle -1(sin^2x-1) =-cos^2x $

Thank you - Mar 11th 2009, 10:19 AMe^(i*pi)
$\displaystyle csc^2(x) = \frac{1}{sin^2(x)}$

$\displaystyle

1- \frac{1}{sin^2(x)} = \frac{sin^2(x) - 1}{sin^2(x)}$

Overall the sum becomes:

$\displaystyle \frac{sin^2(x) - 1}{sin^2(x)csc(x)}$ and so the denominator will be sin(x)

$\displaystyle sin^2(x) - 1 = -cos^2(x) and sin(x) = \sqrt{1-cos^2(x)}$

therefore we have $\displaystyle \frac{-cos^2(x)}{\sqrt{1-cos^2(x)}}$

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From your expression you can say that $\displaystyle -1(sin^2(x)-1) = 1-sin^2(x) = cos^2(x)$ - Mar 11th 2009, 10:26 AMmj.alawami
- Mar 11th 2009, 11:27 AMe^(i*pi)