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If `(2tan^(2)theta_(1)tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(1)tan^(2)theta_(2)+tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(3)tan^(2)theta_(1) = 1` then which of the following relations hold good ?A. `sin^(2)theta_(1) + sin^(2)theta_(2) + sin^(2)theta_(3) = 1`B. `cos2theta_(1) + cos2theta_(2) + cios2theta_(3) = 1`C. `sin^(2)theta_(1) + sin^(2)theta_(2) + sin^(2)theta_(3) = 2`D. `cos2theta_(1) + cos2theta_(2) + cos2theta_(3) = -1` |
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Answer» Correct Answer - A::B divide by `tan^(2)theta_(1)tan^(2)thetatan^(2)theta^(3)` `rArr 2 + cot^(2)theta_(3) + cot^(2)theta_(1) + cot^(2)theta_(2) = cot^(2)theta_(1)cot^(2)theta_(2)cot^(2)theta_(3)` `rArr cosec^(2)theta_(1) + cosec^(2)theta_(2) + cosec^(2)theta_(3)-1` `=(cosec^(2)theta_(1)-1)(cosec^(2)theta_(2)-1)(cosec^(2)theta_(3)-1)` `rArr cosec^(2)theta_(1) cosec^(2)theta_(2)+cosec^(2)theta_(2)cosec^(2)theta_(3)+cosec^(2)theta_(3)cosec^(2)theta_(1)` `= cosec^(2)theta_(1)cosec^(2)theta_(2)cosec^(2)theta_(3)` `sin^(2)theta_(1)+sin^(2)theta_(2)+sin^(2)theta_(3) = 1` (A) of `cos2theta_(1)+cos2theta_(2)+cos2theta_(3) = 1` (B) |
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