Evaluate:
cot0tan(90-0) - (sec(90-0)cosec0 / sin0cos(90-0)+cos0sin(90-0)

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Solution

$\frac{c o t θ \tan (90 - θ) - s e c (90 - θ) \cos e c θ}{\sin θ \cos (90 - θ) + \cos θ \sin (90 - θ)} = \frac{c o t θ c o t θ - \cos e c θ \cos e c θ}{\sin θ \sin θ + \cos θ \cos θ} = \frac{c o t^{2} θ - \cos e c^{2} θ}{\sin^{2} θ + \cos^{2} θ} = \frac{- 1}{1} = - 1$

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J_{0} = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 0 & 0 & 0 & 0 & 0 & 1 0 & 0 & 0 & 0 & 1 & 0 0 & 0 & 0 & 1 & 0 & 0 0 & 0 & 1 & 0 & 0 & 0 0 & 1 & 0 & 0 & 0 & 0 1 & 0 & 0 & 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

I_{0}

P = I_{0} + α J_{0}

α

d e t (P) = 0

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⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & - 1 & 0 & 0 & 0 0 & 0 & 1 & - 1 & 0 0 & 1 & - 1 & 0 & 0 - 1 & 0 & 0 & 0 & 1 0 & 0 & 0 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} 1 & 0 & 0 & 0 0 & 1 & 0 & 0 0 & 0 & 1 & 0 0 & 0 & 0 & 1 \end{matrix} ⎞ ⎟ ⎟ ⎟ ⎠

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