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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
