The value of is Cot17° (Cot73° Cos222° + \(\frac{1}{ \cot 17° \sec^{2}68° } \)) is
1
Let the given expression be denoted by \(E\).
Then, we have
\(E = \cot 17^\circ (\cot 73^\circ \cos^2 22^\circ + \frac{1}{\cot 17^\circ \sec^2 68^\circ})\)
We know that \(\cot x = \tan(90^\circ - x)\) and \(\sec x = \frac{1}{\cos x}\).
Therefore, we can rewrite the expression as:
\(E = \cot 17^\circ (\tan(90^\circ - 73^\circ) \cos^2 22^\circ + \frac{1}{\cot 17^\circ \frac{1}{\cos^2 68^\circ}})\)
\(E = \cot 17^\circ (\tan 17^\circ \cos^2 22^\circ + \frac{\cos^2 68^\circ}{\cot 17^\circ})\)
Since \(\cot x = \frac{1}{\tan x}\), we have \(\cot 17^\circ \tan 17^\circ = 1\).
Also, \(\cos^2 68^\circ = \cos^2 (90^\circ - 22^\circ) = \sin^2 22^\circ\).
Substituting these values into the expression, we get:
\(E = \cot 17^\circ (\tan 17^\circ \cos^2 22^\circ + \frac{\sin^2 22^\circ}{\cot 17^\circ})\)
\(E = \cos^2 22^\circ + \cot 17^\circ \frac{\sin^2 22^\circ}{\cot 17^\circ}\)
\(E = \cos^2 22^\circ + \sin^2 22^\circ\)
Using the identity \(\sin^2 x + \cos^2 x = 1\), we have:
\(E = 1\)
Therefore, the value of the given expression is 1.
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