NAMES: April claims that 1 + = - is an identity for all real numbers 0 that follows from the Pythagorean identity. sin (0) sin (0) a. For which values of 0 are the two functions f (0) = 1 + cos,@ and g(0) = - 1 - defined? sin (0) sin (0) b. Show that the equation 1 + cos (@) 1 sin (0) - follows from the Pythagorean identity. sin (0) C. Is April correct? Explain why or why not. d. Write the equation 1 + Cosz(@) 1 sin (0) - in terms of other trigonometric functions, and state the resulting sin (0) identity. Prove the identity and restrict the domain if needed. csc2 0 = 1 + cot2 0 Recall the Pythagorean identity sin?(0) + cos?(0) = 1, where 0 is any real number. a. Find sin(x), given cos(x) = =, for -?