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Find the general value of `theta` from the equation `tantheta+tan2theta+tan3theta=tantheta*tan2theta*tan3theta.` |
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Answer» `tantheta+tan2theta+tan3theta=tanthetatan2theta tan3theta` `rArr tantheta+tan2theta=-tan3theta+tanthetatan2theta tan3theta=-tan3theta(1-tanthetatan2theta)` `rArr (tantheta+tan2theta)/(1-tanthetatan2theta)=-tan3theta` `rArr tan(theta+2theta)=-tan3theta` `rArr tan3theta=-tan3theta` `rArr 2tan3theta=0` `rArr tan3theta=0` `rArr 3theta=npi` `rArr theta=(npi)/(3)`. Ans. |
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