Question

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to

विकल्प

• 0

• 1

•  −1

• None of these

Answer 1

None of these 

${\displaystyle (\cos ecec\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )}$ Simplifying the given expression, we have 

${\displaystyle (\cos ec\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )}$

${\displaystyle =(\frac{1}{\sin \theta }-\sin \theta )(\frac{1}{{\cos }^2\theta }-\cos \theta )(\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta })}$

${\displaystyle =1-\frac{{\sin }^2\theta }{\sin \theta }\times \frac{1-{\cos }^2\theta }{\cos \theta }\times \frac{{\sin }^2\theta +{\cos }^2\theta }{\sin \theta \cos \theta }}$ 

=${\displaystyle \frac{{\cos }^2\theta }{\sin \theta }\times \frac{{\sin }^2\theta }{\cos \theta }\times \frac{1}{\sin \theta \cos \theta }}$ 

=${\displaystyle \frac{{\cos }^2\theta {\sin }^2\theta }{{\sin }^2\theta {\cos }^2\theta }}$

= ${\displaystyle 1}$