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sin( pi. cos ∂ ) = cos( pi. sin ∂ ) then show that sin 2 ∂ = + 3 / 4 ( the above sign is plus minus)

sin( pi. cos ∂ ) = cos( pi. sin ∂ )
then show that sin 2 ∂ = + 3 / 4
( the above sign is plus minus)

Grade:11

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 years ago

sin( pi. cos ∂ ) = cos( pi. sin ∂ )
sin(pi.cos∂ ) = sin(pi/2+/-pi.sin∂ )
taking + sign
sin(pi.cos∂ ) = sin(pi/2+pi.sin∂ )
pi.cos∂ = pi/2+pi.sin∂
pi.cos∂ -pi.sin∂ =pi/2
cos∂ -sin∂ =1/2
cos2∂ + sin2∂ -2sin∂ cos∂ =1/4
1-sin2∂ =1/4
sin2∂ =3/4
similarly we can prove sin2∂ = -3/4 by taking minus sign

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