Question

Cos 2 180/ 16 +cos 2 540/16 + cos 2 900/16 + cos 2 1260/16 = ?

Answer 1

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

Answer 2

Answer:

2

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

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