Question

How can this be solved?

`tanx/secx` + `cotx/cscx` = `sinx + cosx`

Answer 1

See below.

Explanation:

`LHS`

Identities:

`color(red)bb(tanx=sinx/cosx)` `color(white)(888888)color(red)bb(secx=1/cosx)`

`color(red)(bb(cotx=cosx/sinx)` `color(white)(8888888)color(red)bb(cscx=1/sinx)`

`(sinx/cosx)/(1/cosx)+(cosx/sinx)/(1/sinx)`

`(cosxsinx/cosx)/(cosx1/cosx)+(sinxcosx/sinx)/(sinx1/sinx)`

`(cancelcosxsinx/cancelcosx)/(cancelcosx1/cancelcosx)+(cancelsinxcosx/cancelsinx)/(cancelsinx1/cancelsinx)`

`sinx+cosx`

`LHS-=RHS`

This proves the identity, which is true for all `x`

Identities are proved, not solved.