cos-2-1-cos-2-2-cos-2-3-cos-2-360-

Question Number 144998 by imjagoll last updated on 01/Jul/21

\cos^{2} 1 ° + \cos^{2} 2 ° + \cos^{2} 3 ° + \dots + \cos^{2} 360 ° = ?

Answered by Dwaipayan Shikari last updated on 01/Jul/21

\frac{360}{2} + \frac{1}{2} (c o s 2 ° + c o s 4 ° + c o s 6 ° + \dots + c o s 720 °)

= 180 + \frac{1}{2 \sin (1 °)} (s i n 3 ° - s i n 1 ° + s i n 5 ° - s i n 3 ° + \dots + s i n (721 °) - s i n (719 °))

= 180 + \frac{1}{2 \sin (1 °)} (s i n 721 ° - s i n 1 °) \sin (721 °) = \sin (1 °)

= 180 + 0 = 180 ∵ {c o s}^{2} n ° = \frac{1 + c o s 2 n °}{2}