Question

Express the value of cot theta+tan theta in terms of sec theta and cosec theta

Answer 1

Hey There!!


Here, first we need to know some Trigonometric Relations


$cosec\,\theta = \frac{1}{\sin \theta} \\ \\ \\ \sec \theta = \frac{1}{\cos \theta} \\ \\ \\ \tan \theta = \frac{\sin \theta}{\cos \theta} \\ \\ \\ \cot \theta = \frac{1}{\tan \theta}=\frac{\cos \theta}{\sin \theta}$ 


Also, we need to know one basic identity: 

$\sin^2\theta+cos^2\theta=1$ 


Now we are ready to see your question: 


$\cot \theta + \tan \theta \\ \\ \\ = \frac{\cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta} \\ \\ \\ = \frac{\cos^2\theta+\sin^2\theta}{\cos \theta \sin \theta}\\ \\ \\ = \frac{1}{\cos \theta \sin \theta} \\ \\ \\ = \sec \theta \, cosec\,\theta \\ \\ \\ \\ \implies \boxed{\cot \theta + \tan \theta = \sec \theta \, cosec\, \theta}$



Hope it helps
Purva
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