If π < x <2π,


If $\pi

(a) cosec x + cot x

(b) cosec x − cot x

(c) −cosec x + cot x

(d) −cosec x − cot x


(d) −cosec x − cot x

$\sqrt{\frac{1+\cos x}{1-\cos x}}$

$=\sqrt{\frac{(1+\cos x)(1+\cos x)}{(1-\cos x)(1+\cos x)}}$

$=\sqrt{\frac{(1+\cos x)^{2}}{1-\cos ^{2} x}}$

$=\sqrt{\frac{(1+\cos x)^{2}}{\sin ^{2} x}}$

$=\frac{(1+\cos x)}{-\sin x} \quad[\operatorname{as}, \pi

$=-(\operatorname{cosec} x+\cot x)$

$=-\operatorname{cosec} x-\cot x$

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