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Aline makes acute angle of alpha, beta and gamma with the coordinate axes such that cos alpha cos beta cos gamma = (2)/(9) and cos gammacos alpha = (4)/(9), then cos alpha + cos beta + cos gamma is equal to |
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Answer» `(25)/(9)` `cos alpha cos beta = cos beta cos gamma = (2)/(6)` and `cos gamma cos alpha = (4)/(9)` Then, `cos alpha = (2)/(3), ` `cos beta = (1)/(3)` and `cos gamma = (2)/(3)` `therefore cos alpha + cos beta + cos gamma = (2)/(3) + (1)/(3) + (2)/(3)` `= (5)/(3)` |
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