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If `alpha = sin^(-1)sqrt(3)/(2)+sin^(-1)1/3 , beta =cos ^(-1)sqrt(3)/(2)+cos^(-1)1/3` thenA. `alpha gt beta`B. `alpha = beta`C. `alpha lt beta`D. `alpha + beta` |
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Answer» Correct Answer - C `alpha + beta = sin^(-1)(sqrt(3))/(2) + cos^(-1).(sqrt(3))/(2) +sin^(-1) .(1)/(3)+cos^(-1).(1)/(3)` `=(pi)/(2) +(pi)/(2)=pi` Also `alpha = (pi)/(3) +sin^(-1).(1)/(3) lt (pi)/(3) + sin^(-1).(1)/(2)` As sin `theta` is increasing in `[0,(pi)/(2)]` `therefore " "alpha lt (pi)/(3) +(pi)/(6) = (pi)/(2)` `rArr " "beta gt (pi)/(2) gt alpha` `rArr " "alpha lt beta ` |
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