Question

prove $sin[(2n+1)\pi /2 +- theta] = Cos (theta)$

Answer 1

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cos(2n+1)π/2 is always zero when n€I

For eg:-

When n=1

Cos(2+1)π/2= cos3π/2 = cos270° which equals to 0.

When n=2

Cos(4+1)π/2= cos5π/2= cos450°

= Cos(360+90)°=cos90°=0

When n=-1

Cos(-2+1)/π/2 = cos(-π/2) = cos(-90°)

=Cos(90°) = 0

Hence cos(2n+1)π/2 is always zero

Hope it helps:)

Answer 2

Answer:

cos(2n+1) π / 2 is always zero when

n€l

For example:-

When n=1

Cos × (2 + 1) ×π/ 2 cos 3π/ 2 = cos 270 degrees which equals to 0.

When n = 2

Cos × (4 + 1) × π / 2 = cos 5π/ 2 = cos 450 degrees

=Cos(360+90)° =cos 90° =0

When n = - 1

Cos(-2+1)/ π/2=cos(- π/2)= cos(-90°)

=Cos(90° )=0

Therefore cos(2n+1)π/2 is always zero