1.

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

Answer»

`(25)/(9)`
`(5)/(9)`
`(5)/(3)`
`(2)/(3)`

Solution :GIVEN,
`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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