Alevel (module 2/3 standard). Any help at all would be hugely appriciated.

32. a) Solve in radians

sin (x + pi/6) = 2cosx

giving all solutions in range of 0 < x < 2pi

b) Use the formular tan (a - b) = (tana - tanb)/(1 + tana tanb)

to show that tan(x - pi/4) = (tanx - 1)/(tan x+1)

c) Hence or otherwise solve in radians tan(x - pi/4) = 6tanx

67. Betweem -180 < x < 180 solve

cosec^2 x = 1 + 2 sec^2 x

68. For all values of x prove that

8 sin^4 x = 3 - 4 cos 2 x + cos 4 x

Hence find in radians in terms of pi the values of x in pi and -pi for which cos 4x - 4cos 2x + 1 = 0

70. Find the values of x for 0-360 for which tan^2 x + 2 sec x = 5

85. Find values to which

3 cos 2x + 7 cos x = 0 and 0 < x < 2pi

Thank you for reading. xx