Question

prove that :-cos π/5 + cos 3π/5=1/2​

Answer 1

Answer:

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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Answer 2

Cos π/5 =0.80

Cos π/5 =0.80Cos 3π/5 = -0.30

Cos π/5 =0.80Cos 3π/5 = -0.30Cos π/5+Cos 3π/5

Cos π/5 =0.80Cos 3π/5 = -0.30Cos π/5+Cos 3π/5=0.80-0.30

Cos π/5 =0.80Cos 3π/5 = -0.30Cos π/5+Cos 3π/5=0.80-0.30=0.50

Cos π/5 =0.80Cos 3π/5 = -0.30Cos π/5+Cos 3π/5=0.80-0.30=0.50=1/2 [PROVED]