Find the value of x if $x = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi}$. Find the value of x if $x = \dfrac{1 + \tan^2 \varphi}{\tan \varphi \, \csc^2 \varphi}$. A. $\sin \varphi$ C. $\tan \varphi$ B. $\cos \varphi$ D. $\csc \varphi$ Log in or register to post comments Solution Click here to… Jhun Vert Fri, 06/07/2024 - 21:07 Solution Click here to expand or collapse this section $\begin{align} x & = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi} \\ \\ & = \dfrac{\sec^2 \phi}{\tan \phi \, \csc^2 \phi} \\ \\ & = \dfrac{\dfrac{1}{\cos^2 \phi}}{\dfrac{\sin \phi}{\cos \phi} \cdot \dfrac{1}{ \, \sin^2 \phi}} \\ \\ & = \dfrac{\dfrac{1}{\cos^2 \phi}}{\dfrac{1}{\sin \phi \, \cos \phi}} \\ \\ & = \dfrac{\dfrac{1}{\cos \phi}}{\dfrac{1}{\sin \phi}} \\ \\ & = \dfrac{\sin \phi}{\cos \phi} \\ \\ & = \tan \phi \end{align}$ Log in or register to post comments
Solution Click here to… Jhun Vert Fri, 06/07/2024 - 21:07 Solution Click here to expand or collapse this section $\begin{align} x & = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi} \\ \\ & = \dfrac{\sec^2 \phi}{\tan \phi \, \csc^2 \phi} \\ \\ & = \dfrac{\dfrac{1}{\cos^2 \phi}}{\dfrac{\sin \phi}{\cos \phi} \cdot \dfrac{1}{ \, \sin^2 \phi}} \\ \\ & = \dfrac{\dfrac{1}{\cos^2 \phi}}{\dfrac{1}{\sin \phi \, \cos \phi}} \\ \\ & = \dfrac{\dfrac{1}{\cos \phi}}{\dfrac{1}{\sin \phi}} \\ \\ & = \dfrac{\sin \phi}{\cos \phi} \\ \\ & = \tan \phi \end{align}$ Log in or register to post comments
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