Answer:
[tex]\sec^2(\alpha)=1+\tan^2(\alpha)[/tex]
[tex]\csc^2(\alpha)=1+\cot^2(\alpha)[/tex]
[tex]\cot^2(\alpha)=\dfrac{1}{\tan^2(\alpha)}[/tex]
[tex]\begin{aligned}\sec^2(\alpha) \cdot \csc^2(\alpha) & = (1+\tan^2(\alpha))(1+\cot^2(\alpha))\\\\ & =1+\cot^2(\alpha)+\tan^2(\alpha)+tan^2(\alpha)\cot^2(\alpha)\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+\tan^2(\alpha) \cdot \dfrac{1}{\tan^2(\alpha)}\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+ \dfrac{\tan^2(\alpha)}{\tan^2(\alpha)}\\\\& = 1+\cot^2(\alpha)+\tan^2(\alpha)+1\\\\& = \tan^2(\alpha)+\cot^2(\alpha)+2\end{aligned}[/tex]
Answer:
See below ~
Step-by-step explanation:
Trigonometric Identies (needed)
Solving
Expanding the LHS
∴ Hence, we have proved the left hand side of the equation is equal to the right hand side.
