Question

$\frac{\cot (90°-\theta )\sin (270°+\theta )\text{cosec}(180°+\theta )}{\cos (-\theta )\sin (90°+\theta )\tan (360°-\theta )}$ is equal to

• A. $\sec \theta \text{cosec}\theta$
• B. $-\sec \theta \text{cosec}\theta$
• C. $-\text{cosec}\theta$
• D. $\sec \theta$

Answer 1

The correct option is B $-\sec \theta \text{cosec}\theta$

$\frac{\cot (90°-\theta )\sin (270°+\theta )\text{cosec}(180°+\theta )}{\cos (-\theta )\sin (90°+\theta )\tan (360°-\theta )}$
$=\frac{\tan \theta (-\cos \theta )(-\text{cosec}\theta )}{\left(\cos \theta \right)\left(\cos \theta \right)(-\tan \theta )}$
$=-\sec \theta \text{cosec}\theta$