UP Board Class 10 maths Paper set 822 (AV) solution 3 (a)

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3(a). In English
 Prove that cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8 = 0
Solution: cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8
              =  cos π/8 +cos 7π/8+ cos 3π/8 +cos 5π/8
              =  cos(π − 7π/8) +cos 7π/8+ cos 3π/8 +cos (π − 3π/8)
              = − cos 7π/8 +cos 7π/8 + cos 3π/8 −  cos 3π/8
              = 0

3(a). In Hindi
 fl) dhft, fd  cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8 = 0
Solution: cos π/8 + cos 3π/8 +cos 5π/8 +cos 7π/8
              =  cos π/8 +cos 7π/8+ cos 3π/8 +cos 5π/8
              =  cos(π − 7π/8) +cos 7π/8+ cos 3π/8 +cos (π − 3π/8)
              = − cos 7π/8 +cos 7π/8 + cos 3π/8 −  cos 3π/8
              = 0
                  

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