Question

I’m supposed to prove this but it doesn’t work for me help

Answer 1

we have the equation

`(cotx+tanx)^2=csc^2x+sec^2x`

Remember that

`\begin{gathered} tan^2x+1=sec^2x \\ cot^2x+1=csc^2x \end{gathered}`
`\begin{gathered} tanx=(sinx)/(cosx) \\ \\ cotx=(cosx)/(sinx) \end{gathered}`

substitute

`(cotx+tanx)^2=((cosx)/(sinx)+(sinx)/(cosx))^2=((cos^2x+sin^2x)/(sinxcosx))^2=((1)/(sinxcosx))^2=(cscxsecx)^2`

and

`(cscxsecx)^2=csc^2x*sec^2x`

substitute the identity

`csc^2x*sec^2x=(cot^2x+1)(tan^2x+1)=cot^2xtan^2x+cot^2x+tan^2x+1)=sec^2x+csc^2x`

Remember that

`cot^2xtan^2x=1`

therefore

`sec^2x+csc^2x=sec^2x+csc^2x\text{ -----> is proved}`