Question

How do you prove `tanx + cotx = secx cscx`?

Answer 1

Please follow the step below

Explanation:

Given:
`tan x+ cot x= sec x *cscx`

Start on the right hand side, change it to `sinx` ; `cosx`

`sinx/cosx + cosx/sinx = sec x *csc x`

`color(red)([sinx/sinx])*(sinx/cosx)` + #color(blue) [cosx/cosx]*cosx/sinx# = `sec x*cscx`

`[sin^2x+cos^2x]/(sinx*cosx) = sec x *cscx`

`1/(sinx *cos x) = sec x *csc x`

`(1/sinx)(1/cosx) = secx*cscx`

`sec x *csc x = secx *csc x`

Prove completed!

*`sin^2x + cos^2x= 1`

*`1/sinx = csc x` ; `1/cosx = secx`