Answer:
[tex]cotg^{2} \theta[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{csc\theta (ctg\theta)}{sec\theta}[/tex]
But, we know that:
[tex]csc\theta=\frac{1}{sin\theta}[/tex]
[tex]ctg\theta = \frac{cos\theta}{sin\theta}[/tex]
[tex]sec\theta=\frac{1}{cos\theta}[/tex]
Replacing all these basic identities in the given expression, we have:
[tex]\frac{csc\theta (ctg\theta)}{sec\theta}\\\frac{\frac{1}{sin\theta}\frac{cos\theta}{sin\theta}}{\frac{1}{cos\theta}}\\\frac{cos^{2}\theta}{sin^{2} \theta }\\(\frac{cos\theta}{sin\theta})^{2}\\cotg^{2} \theta[/tex]
