Some of these already have answers. Can you just give me a clear explanation without using cursive?

1. Prove the following identities: (a) secr - cosr = tan rsinc (b) sin( + y) sin(x - y) = sin x - sin y 2. If cos 0 3 7, 7 0- 27, find tan 0 and sin 20 without using a calculator. Answer: tan 0 = V7 3V7 3 -, sin 20 = 8 13 3. If tanx = and secy = ], where r and y lie between a and 27, evaluate csc(x -y) 13 \ 10 and cos 2r. Answer: csc(x - y) = 27 coS 2 = 4. Find all values of a in [0, 2x] that satisfy the equation: 5 cosr - 2 sin'x = 1 Answer: r = 3' 3 5. Determine if the following functions are one-to-one, even, odd, periodic. (a) f(x) = x2 -10r+ 1 Answer: Not one-to-one, Neither even nor odd, not periodic (b) f(x) = - sin 2x, x E (-7, ") Answer: Not one-to-one, not even, odd, not periodic (c) f(x) = In(2x - 2) -5 Answer: one-to-one, neither even nor odd, not periodic 6. Find a formula for the inverse of the given function. Also find the domain and range of f and f-. 3. + 2 (a) f(x) = 9.x - 2 -r+9 Answer: f (x) = 3+ , dom f-range f-1= (-00, 9) U(9, 00) domain f -range f= (-0o, -3) U (-3, 00)1 (b) f(x) = V20x -5 Answer: f (x) = 20 (x2 + 5), dom f-range f-1= [1/4, 00) dom f -range f= [0, co) 7. Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and applying the appropriate transformations. (a) y = v2 +4-2 (b) y= ex-2+1 8. Find f + 9, fg, gof, and fog where f(x) = - and g(r) = sin 3r - Vr + 1 sin 3x - Vr +1 Answer: (f + 9) (x) = - -+ sin 3x - vr +1, (fg)(x) = (go f)(x) = sin +1, (fog)(x) sin 3x - Vr +1