InterviewSolution
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InterviewSolution
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If `alpha+beta=pi/2` and `beta+gamma=alpha` then `tanalpha` equalsA. `2(tan beta + tan gamma)`B. `tan beta + tangamma`C. `tanbeta + 2tan gamma`D. `2tan beta + tan gamma` |
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Answer» Correct Answer - c Given, `alpha+beta=pi//2` `implies alpha=(pi//2)-beta` `implies tan alpha = tan (pi//2-beta)` `implies tan alpha = cot beta` `implies tan alpha tan beta = 1` Again, `beta + gamma = alpha " [given]"` `implies gamma = (alpha - beta)` `implies tan gamma = tan(alpha - beta)` `implies tan gamma = (tanalpha-tanbeta)/(1+tanalphatanbeta)` `implies tan gamma = (tan alpha-tanbeta)/(1+1)` `therefore 2 tan gamma = tan alpha - tan beta` `implies tan alpha=tanbeta + 2 tan gamma` |
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