InterviewSolution
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InterviewSolution
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Vectors `vecA` and `vecB` include an angle `theta` between them. If `(vecA + vecB)` and `(vecA- vecB)` respectively subtend angles `alpha and beta` with `vecA`, then `(tan alpha + tan beta)` isA. `((A sin theta))/((A^(2) +B^(2)cos^(2)theta)) `B. `((2AB sin theta))/((A^(2) -B^(2)cos^(2)theta)) `C. `((A^(2) sin^(2) theta))/((A^(2) +B^(2)cos^(2)theta)) `D. `((B^(2) sin^(2) theta))/((A^(2) -B^(2)cos^(2)theta)) ` |
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Answer» Correct Answer - B `tan alpha = (B sin theta)/(A + B cos theta)" "…(i)` where `alpha ` is the angle made by the vector `(vecA + vecB)` with `vecA`. Similarly, `tan beta = (B sin theta)/(A - B cos theta) " "…(ii)` where `beta` is the angle made by the vector `(vecA - vecB)` with `vecA`. Note that the angle between `vecA and (-vecB)` is `(180^(@) - theta)`. Adding (i) and (ii), we get `tan alpha + tan beta = (B sin theta)/(A + b cos theta) + (B sin theta)/(A -Bcostheta)` ` = (AB sin theta - B^(2) sin thetacos theta + AB sin theta + B^(2) sintheta cos theta)/((A + B cos theta)(A-Bcos theta))` ` = (2AB sin theta)/((A^(2) - B^(2) cos ^(2) theta))` |
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