Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0) + C ○ sec³ (0) - sec³ (0) + C O sec (0) - sec³ (0) + sec³ (0) + C

Find the derivative

[(2tan(x)/1+sec(x))+(2+2sec(x)/tan(x))]=4csc(x)

1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative. You may not use the formula for the derivatives of sine or cosine. Hint: use the sum formula: and the identity: tan(x + y) = tan(x) + tan(y) 1 tan(x) tan(y) 1 + tan²(x) = sec²(x).