InterviewSolution
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InterviewSolution
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यदि `cos^(-1)x + cos^(-1)y + cos^(-1) z = x`, सिद्ध करे कि `x^(2) + y^(2) + z^(2) + 2xyz = 1.` |
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Answer» माना कि, `cos^(-1) x = alpha, cos^(-1) y = beta` तथा `cos^(-1) z = gamma ` `rArr cos alpha = x, cos beta = y` तथा `cos gamma = z ` प्रश्न से, `alpha + beta + gamma = pi therefore alpha + beta = pi -gamma` `therefore cos (alpha + beta) = cos (pi-gamma)` या, `cos alpha cos beta - sin alpha sin beta = - cos gamma` या, `xy-sqrt(1-x^(2)) sqrt(1-y^(2)) = -z` या, `xy + z = sqrt(1-x^(2)) sqrt(1-y^(2))` दोनों तरफ करने पर, `x^(2) y^(2) + z^(2) + 2xyz = 1 - x^(2) - y^(2) + x^(2) y^(2)` या, `x^(2) + y^(2) + z^(2) + 2xyz = 1` |
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