Question

Find the value of $\left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right)$.

Answer 1

Given data: $\left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right)$

Finding the value of $\left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right)$:

$$\begin{gathered} \left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right) \\ =7\left(\frac{1}{{\displaystyle \frac{{\cos }^2\theta }{{\sin }^2\theta }}}-\frac{1}{{\cos }^2\theta }\right) \\ =7\left(\frac{{\sin }^2\theta }{{\cos }^2\theta }-\frac{1}{{\cos }^2\theta }\right) \\ =7\left(\frac{{\sin }^2\theta -1}{{\cos }^2\theta }\right) \\ =-7\left(\frac{1-{\sin }^2\theta }{{\cos }^2\theta }\right) \\ =-7\left(\frac{{\cos }^2\theta }{{\cos }^2\theta }\right) \\ =-7 \end{gathered}$$

Hence, the value of $\left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right)=-7$.