The value of 152 (sin 30° + 2 cos² 45° + 3 sin 30°

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The value of 152 (sin 30° + 2 cos² 45° + 3 sin 30° + 4 cos² 45° + .... + 17 sin 30°+ 18 cos² 45°) is

1. an integer but not a perfect square
2. a rational number but not an integer
3. a perfect square of an integer
4. irrational

152 (sin 30° + 2 cos² 45° + 3 sin 30° + 4 cos² 45° + .... + 17 sin 30° + 18 cos² 45°)

It is an A.P. whose a =		1	, d =	1	, n = 18
		2		2

=	152 × 9 × 19	= 12996 and √12996 = 114
	2

i.e. a perfect square of an integer.