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cos^-1(x)+cos^-1(y)=beta prove that x^2-2xycosbeta+y^2=sin^2beta

cos^-1(x)+cos^-1(y)=beta
prove that x^2-2xycosbeta+y^2=sin^2beta
 

Grade:12

1 Answers

Amit
405 Points
6 years ago
Apply cos both side and open cos(cos-¹x+cos-¹y) using cos(a+b) formula . Write sin(cos-¹x)=sqrt(1-x²) and similar for other .. now take sqrt(1-x²).sqrt(1-y²) on other side and bring cos(beta) on the initial side. Now square and rearrange.

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