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The sum of all solutions in $[0, 4 π]$ of the equation $\tan + \cot x + 1 = \cos (x + \frac{π}{4})$ is

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Correct option is C

We have tanx+cotx=cosx+π4−1tanx+cotx≤−2 and cosx+π4−1≥−2It implies that equality holds when both are −2cosx+π4=−1⇒x+π4=(2n+1)π,n∈z⇒x=3π4 or 11π4⇒sum=7π2

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The sum of all solutions in 0,4π of the equation tan+cotx+1=cosx+π4 is

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The sum of all solutions in $[0, 4 π]$ of the equation $\tan + \cot x + 1 = \cos (x + \frac{π}{4})$ is