InterviewSolution
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InterviewSolution
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If `a_(1), a_(2), …..,a_(n)` are in A.P. with common difference `d ne 0,` then the sum of the series sin `d[sec a_(1)sec a_(2) +..... sec a_(n-1) sec a_(n)]` isA. `cosec a_(n)-cosec a`B. `cot a_(n)-cot a`C. `sec a_(n)- sec a_(1)`D. `tan a_(n)- tan a_(1)` |
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Answer» Correct Answer - D As `a_(1),a_(2),a_(3),…,a_(n-1),a_(n)` are in A.P., hence `d=a_(2)-a_(1)=a_(3)-a_(2)=…=a_(n)-a_(n-1)` `sind[seca_(1)seca_(2)+seca_(2)seca_(3)+…+seca_(n-1)seca_(n)]` `=(sin(a_(2)-a_(1)))/(cosa_(1)cosa_(2))+(sin(a_(3)-a_(2)))/(cosa_(2)cosa_(3))+...+(sin(a_(n)-a_(n-1)))/(cosa_(n-1)cosa_(n))` `=(tana_(2)-tana_(1))+(tana_(3)-tana_(2))+...+(tana_(n)-tana_(n-1))` `=tana_(n)-tana_(1)` |
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