Question

prove 1-cosx=2sin^2 x/2

Answer 1

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нєяє ιѕ уσυя αиѕωєя уσυя ωαιтιиg fσя :


αиѕωєя:

Given ;

1+cos(x)= 2cos^2(x/2)

Taking the left hand side first,

=>LHS= 1+cos(x)

We know that,

=>Cos(2a)= 2cos^2(a)-1

(One of the trigonometric identities )

Taking a=x/2,we get

=>Cos(2x/2)=2cos^2(x/2)-1

=>Cos(x)=2cos^2(x/2)-1

Substituting this value in LHS,we get

=>1+cos(x)=1+(2cos^2(x/2)-1)

1+cos(x)=2cos^2(x/2)=RHS


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