Question

Number of values of $\theta ϵ[0,2\pi ]$ satisfying the equation $\cot x-\cos x=1-\cot x.\cos x$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$\frac{cosx}{sinx}-cosx=1-\frac{co{s}^{2}x}{sinx}$

$\Rightarrow cosx-cosx\ast sinx=sinx-co{s}^{2}x$

$\Rightarrow co{s}^{2}x+cosx-cosxsinx-sinx=0$

$\Rightarrow cosx(1+cosx)-sinx(1+cosx)=0$

$\Rightarrow (cosx-sinx)(1+cosx)=0$

$\Rightarrow x=\frac{\pi }{4},\frac{5\pi }{4},\pi$

Hence, 3 solutions exist.