InterviewSolution
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InterviewSolution
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If `a^2, b^2,c^2`are in A.P., then prove that `tanA ,tanB ,tanC`are in H.P. |
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Answer» `a^(2), b^(2), c^(2)` are in A.P. `rArr b^(2) - a^(2) = c^(2) - b^(2)` `rArr sin^(2)B - sin^(2) A = sin^(2) C - sin^(2) B` (Using sine Rule) or `sin(B + A) sin (B - A) = sin (C + B) sin (C - B)` or `sin C (sin B cos A - cos B sin A)` `= sin A (sin C cos B - cos C sin B)` Dividing both sides by sin A sin B sin C, we get `cot A - cot B = cot B - cot C` `rArr cot A, cot B, cot C` are in A.P. `rArr tan A, tan B, tan C` are in H.P. |
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