Question

Prove the following 1+tanA/sinA+1+cotA/cosA=2cosecA?

Answer 1

Not an identity, see below

Explanation:

`(1+tanA)/sinA+(1+cotA)/cosA=2cscA`

`(cosA(1+tanA))/(sinAcosA)+(sinA(1+cotA))/(cosAsinA)=2cscA`

`(cosA+tanAcosA)/(sinAcosA)+(sinA+cotAsinA)/(cosAsinA)=2cscA`

Apply quotient identities: `tanx=sinx/cosx` and `cotx=cosx/sinx`:

`(cosA+sinA/cosAcosA)/(sinAcosA)+(sinA+cosA/sinAsinA)/(cosAsinA)=2cscA`

`(cosA+sinA)/(sinAcosA)+(sinA+cosA)/(cosAsinA)=2cscA`

`1/sinA+1/cosA+1/cosA+1/sinA= 2cscA`

Reciprocal identities: `1/cosx=secx` `1/sinx=cscx`:

`2cscA+2secA=2cscA` Not quite accurate