Question

Cos^2(180/16)+cos^2(3×180/16)+cos^2(5×180/16)+cos^2(7×180/16)

Answer 1

Step-by-step explanation:

cos²180°/16+cos²540°/16+cos²900°/16+cos²1260°/16

=cos²π/16+cos²3π/16+cos²5π/16+

cos²7π/16 [180°/16=π/16 (say)]

=cos²π/16+cos²3π/16+cos²(π/2-3π/16)+cos²(π/2-π/16)

=cos²π/16+cos²3π/16+sin²3π/16+sin²π/16 [∵ cos(π/2-Ф)=sinФ]

=(sin²π/16+cos²π/16)+(sin²3π/16+cos²3π/16)

=1+1 [∵ sin²Ф+cos²Ф=1]

=2