Question

सिद्ध कीजिए कि
` cos^(-1)x+cos^(-1)""((x)/(2)+(1)/(2)sqrt(3-3x^(2)))=(pi)/(3)`

Answer 1

माना `cos^(-1)x=thetaimplies x=cos theta `
तथा ` sqrt(1-x^(2))=sqrt(1-cos^(2)theta)=sin theta `
अब , माना
बायाँ पक्ष
`= cos^(-1)x+cos^(-1)((x)/(2)+(sqrt(3))/(2)sqrt(1-x^(2)))`
`=theta+cos^(-1)(cos""(pi)/(3)*cos theta+sin""(pi)/(3)*sin theta)`
`= theta + cos^(-1)[cos""((pi)/(3)-theta)]=theta+((pi)/(3)-theta)`
`= (pi)/(3)=` दायाँ पक्ष