InterviewSolution
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InterviewSolution
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`sin alpha+ sinbeta=(1)/(4)` and `cos alpha+cos beta=(1)/(3)` The value of `tan (alpha+beta)` isA. `(25)/(7)`B. `(25)/(12)`C. `(25)/(13)`D. `(24)/(7)` |
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Answer» Correct Answer - D `sin alpha + sin beta = (1)/(4)" "`...(i) `rArr 2 sin((alpha + beta)/(2)) cos ((alpha -beta)/(2))= (1)/(4)" "`...(ii) `rArr cosalpha + cos beta = (1)/(3)" " `...(iii) `rArr 2 cos ((alpha + beta )/(2) ) cos((alpha -beta) /(2)) = (1)/(3)" "` (iv) Dividing Eq. (ii) by Eq. (iv), we have `" " tan((alpha + beta) /(2)) = (3)/(4)` `rArr sin(alpha + beta) = (2tan((alpha + beta)/(2)))/(1+tan^(2)((alpha + beta)/(2)))` `" " = (2xx (3)/(4))/(1+((3)/(4))^(2)) = (24)/(25)` `therfore cos (alpha + beta) = (7)/(25) and tan(alpha + beta) = (24)/(7)` |
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