Number of values of x ∈ left[ {0,2π } right] satisfying equation cotx - cosx = 1 - cotx. co

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3.Trigonometrical Ratios, Functions and Identities

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Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$

A

$1$

B

$3$

C

$2$

D

$4$

Solution

$\cot x-\cos x=1-\cot x \cos x$

$1-\cot x+\cos x-\cot x \cos x=0$

$(1-\cot x)(1+\cos x)=0$

$\therefore \cot x=1$ or $\cos x=-1$

$x=n \pi+\frac{\pi}{4}$ or $x=(2 n+1) \pi$

$\therefore$ Solution set $=x: x=2 n \pi+\pi, n \in I \cup x: x=2 n \pi+\frac{\pi}{4}, n \in I$

Standard 11

Mathematics

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