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Solve for x :
cos2 30° + sin2 2x = 1
sin2 60° + cos2 (3x - 9°) = 1
If 4 cos2 x = 3 and x is an acute angle; find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x
(iv) sin 2x
If 2 cos (A + B) = 2 sin (A - B) = 1; find the values of A and B.