Question

Hi! pleas click the image, if possible, please explain how I can prove this trigonometric identity?

Answer 1

Given trigonometric identity to prove:

`(\cos^2t+4\cos t+4)/(\cos t+2)=(2\sec t+1)/(\sec t)`

Take Left hand side of the equation:

`\begin{gathered} (\cos^2t+4\cos t+4)/(\cos t+2)=(\cos ^2t+2*2*\cos t+2^2)/(\cos t+2) \\ =((\cos t+2)^2)/(\cos t+2) \\ =\cos t+2 \end{gathered}`

Take Right hand side of the equation:

`\begin{gathered} (2\sec t+1)/(\sec t)=((2)/(\cos t)+1)/((1)/(\cos t)) \\ =((2+\cos t)/(\cos t))/((1)/(\cos t)) \\ =\cos t+2 \end{gathered}`

So, we have LHS = RHS.

Hence, proved.