The value of m[sinθ + 2cos2∅ + 3sinθ + 4cos2∅ + . . . . . . . . + 18c…

Question

The value of m[sinθ + 2cos2∅ + 3sinθ + 4cos2∅ + . . . . . . . . + 18cos2∅] is a perfect square of an integer, θ = 30°, ∅ = 45° and 150 ≤ m ≤ 180. Find the value of m.

Accepted Answer

Option C. 152. Answer & Solution Answer: Option C Solution: & m [ + 2 ^2 + 3 + 4 ^2 + \,.....\,18 ^2 ] & = 30^ ,\,\, = 45^ & = m [ ( + 3 + 5 + \,.....\,17 ) + ( 2 ^2 + 4 ^2 + \,.....\,18 ^2 ) ] & Sum of odd number = ( 9 )^2, & Sum of even number = 9 × 10 & = m [ 81 + 90 ^2 ] & = m [ 81 × 30 +…