Question

Prove the following identity please ls=rs state restrictions grade 12 math

Answer 1

We have to prove this identity.

We will use the right side and rearrange it into the left side.

We can do it as:

`\begin{gathered} 2(\cos^4x)/(\sin2x)-\cos^2x\cdot\csc2x-(2\sin^2x\cdot\cos^2x)/(\sin2x)+\sin^2x\cdot\csc2x \\ \\ (\cos^2x-\sin^2x)((2\cos^2x)/(\sin2x)-\csc2x) \\ \\ (\cos2x)((2(\cos2x+\sin^2x))/(\sin2x)-(1)/(\sin2x)) \\ \\ (\cos2x)(2(\cos2x)/(\sin2x)+2(\sin^2x)/(\sin2x)-(1)/(\sin2x)) \\ \\ (\cos2x)(2\cot2x+(2)/(\sin2x)((1-\cos2x)/(2))-(1)/(\sin2x)) \\ \\ (\cos2x)(2\cot2x+(1-\cos2x)/(\sin2x)-(1)/(\sin2x)) \\ \\ (\cos2x)(2\cot2x+(1)/(\sin2x)-(\cos2x)/(\sin2x)-(1)/(\sin2x)) \\ \\ (\cos2x)(2\cot2x-(\cos2x)/(\sin2x)) \\ \\ (\cos2x)(2\cot2x-\cot2x) \\ \\ (\cos2x)(\cot2x) \end{gathered}`