InterviewSolution
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InterviewSolution
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यदि `cos^(-1)x+cos^(-1)y+cos^(-1) z = pi`, तब सिद्ध कीजिए - `x^(2)+y^(2)+z^(2)+2xyz=1`. |
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Answer» यहाँ `cos^(-1)x+cos^(-1)y+cos^(-1)z=pi` `rArr " " cos^(-1)x + cos^(-1)y =pi - cos^(-1)z` `rArr cos^(-1)(xy - sqrt(1-x^(2))sqrt(1-y^(2)))=cos^(-2)(-z), " " [because cos^(-1)(-z)=pi-cos^(-1)z]` `rArr " " xy - sqrt(1-x^(2))sqrt(1-y^(2))= -z` `rArr " " xy+z=sqrt(1-x^(2))sqrt(1-y^(2))` दोनों पक्षों का वर्ग करने पर, `(xy+z)^(2)=(1-x)^(2)(1-y^(2))` `rArr x^(2)y^(2)+z^(2)+2xyz=1-x^(2)-y^(2)+x^(2)y^(2)` `rArr " " x^(2)+y^(2)+z^(2)+2xyz=1`. यही सिद्ध करना था | |
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