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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) is |
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Answer» `((A sin theta))/((A^(2) +B^(2)cos^(2)theta)) ` 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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