Question

Verify:
`(1)/(tanx) + tanx = (sec^(2)x )/(tanx)`

Answer 1

Explanation:

`(1+tan^(2) x )/(tanx) =(sec^(2) )/(tanx) \\divide \ each \ side \ with \ tanx,\\1+tan^(2) x=sec^(2)`

`tan^(2) x=(sec^(2) x)/(cos^(2) x) \\1+(sec^(2) x)/(cos^(2) x) \\=sec^(2) x\\(cos^(2) x)/(cos^(2) x) +(sec^(2) x)/(cos^(2) x)=(cos^(2) x+sec^(2)x )/(cos^(2) x) \\which \ we \ know \ cos^(2) x+sec^(2)x =1\\so,(cos^(2) x+sec^(2)x )/(cos^(2) x) =1/cos^(2) x=sec^(2) x\\sec^(2) x*cos^(2) x=1`