If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.
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If 3 tan2 θ - 1 = 0, find cos 2θ, given that θ is acute.
If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.
If sin 3x = 1 and 0° ≤ 3x ≤ 90°, find the values of
(i) sin x
(ii) cos 2x
(iii) tan2 x - sec2 x.