Question

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

Answer 1

Answer:

let's start.

Step-by-step explanation:

                         $\frac{(1+tanx)}{sinx} -secx = cscx$

we can write it as

                        $\frac{(1 + tanx)}{sinx} = cscx + secx$

starting with left hand side

LHS    

       $\frac{(1 + tanx)}{sinx}$

      $\frac{1}{sinx} + \frac{tanx}{sinx}\\\\cscx + tanx *\frac{1}{sinx}\\\\cscx + \frac{sinx}{cosx} *\frac{1}{sinx}\\\\cscx + \frac{1}{cosx}\\\\cscx + secx$  

       

∴ LHS = RHS

hence,   proved        

Answer 2

Answer:

See below

Step-by-step 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