Question

How to know which double angle COS formula to substitute in and why. Also if I should leave CSC^2 as it is or if I should change it to 1/SIN^2 to solve

Answer 1

It is given that:-

`\begin{gathered} \csc ^2\beta*\cos (2\beta) \\ =(1)/(\sin^2\beta)*(\cos ^2\beta-\sin ^2\beta) \\ =(\cos^2\beta)/(\sin^2\beta)-(\sin ^2\beta)/(\sin ^2\beta) \\ =\cot ^2\beta-1 \end{gathered}`

So the correct answer is

`\cot ^2\beta-1`