Question

Demontrons que
Cosπ/5+cos3π/5=1/2

Answer 1

Answer:

Step-by-step explanation:

cosA + cosB = 2cos[(A+B)/2] cos[(A-B)/2] ........................ identity

=> cos(π/5) + cos(3π/5)

= 2cos(2π/5) cos(π/5)

= 2cos(π/5) sin(π/5) cos(2π/5) / sin(π/5) ... [multiplying numerator and denominator by sin(π/5)]

= sin(2π/5) cos(2π/5) / sin(π/5)

= 2sin(2π/5) cos(2π/5) / 2sin(π/5)

= sin(4π/5) / 2sin(π/5)

= sin(π - π/5) / 2sin(π/5)

= sin(π/5) / 2sin(π/5)

= 1/2.

Hope it helps...

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