Question

Verify [(1+tanx)/sinx] - secx = cscx. Show your work and identities you used.

Answer 1

let's start.

Explanation:

`((1+tanx))/(sinx) -secx = cscx\\`

we can write it as

`((1 + tanx))/(sinx) = cscx + secx`

starting with left hand side

LHS

`((1 + tanx))/(sinx)`

`(1)/(sinx) + (tanx)/(sinx)\\\\cscx + tanx *(1)/(sinx)\\\\cscx + (sinx)/(cosx) *(1)/(sinx)\\\\cscx + (1)/(cosx)\\\\cscx + secx`

∴ LHS = RHS

hence, proved

Answer 2

See below

Explanation:

• (1 + tanx)/sinx - secx = cscx
• 1/ sinx + tanx/ sinx - 1/cosx = cscx
• 1/ sinx + sinx/ cosx × 1/sinx - 1/ cos x = cscx
• 1/ sinx + 1/cosx - 1/cosx = cscx
• 1/ sinx = cscx
• cscx = cscx