Question

Find the value of cos² π/8 + cos² 3π/8 + cos² 5π/8 + cos² 7π/8.

Answer 1

Answer:-

Cos² (π/8) + Cos² (3π/8) + Cos² (5π/8) + Cos² (7π/8) = 2

Taking L.H.S. -

= Cos² (π/8) + Cos² (3π/8) + Cos² (5π/8) + Cos² (7π/8)

= Cos² (π/8) + Cos² (π/2 - π/8) + Cos² (5π/8) + Cos² (3π/2 + 5π/8)

= Cos² (π/8) + {-Sin (π/8)}² + Cos² (5π/8) + Sin² (5π/8)

= Cos² (π/8) + Sin² (π/8) + Cos² (5π/8) + Sin² (5π/8)

= 1 + 1

= 2.

(R.H.S.)

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Answer 2

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