Prove the trigonometric identity tan^2(x)+1=sec^2(x)

 We can start with the identity sin²(x)+cos²(x)=1 If we divide through the equation by cos²(x), we get: sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x) If we look at the left hand side of the equation: sin²(x)/cos²(x) is equal to tan²(x), and cos²(x)/cos²(x) is equal to 1 (as it is divided through by itself), the left hand side becomes tan²(x) +1 Now if we look at the right hand side of the equation: 1/cos²(x) is equal to sec²(x) Putting both sides of the equation together, we get tan²(x) +1=sec²(x)