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To show that

cos-1(-x)-cos-1(x)=2sin-1(x)

I tried

take x= sina

taking cos of the whole equation

cos(cos-1(-x))-cos(cos-1(x))=2cos(sin-1(x))

now we have to prove : -x-x=2cos(sin-1(x))

LHS: -2x=-2sina=2cos(a+pi/2)

RHS: 2cosa

Iam not sure how to proceed further..can anyone help me with this..

cos-1(-x)-cos-1(x)=2sin-1(x)

I tried

take x= sina

taking cos of the whole equation

cos(cos-1(-x))-cos(cos-1(x))=2cos(sin-1(x))

now we have to prove : -x-x=2cos(sin-1(x))

LHS: -2x=-2sina=2cos(a+pi/2)

RHS: 2cosa

Iam not sure how to proceed further..can anyone help me with this..

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