InterviewSolution
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InterviewSolution
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If a `costheta-bsintheta=c ,`prove that a `sintheta+bcostheta=+-sqrt(a^2+b^2-c^2)` |
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Answer» Given, ` a cos theta - b sin theta = c. " "...(i) ` Now, ` (a cos theta - b sin theta)^(2) + (a sin theta + b cos theta)^(2) ` `=a^(2) (cos^(2) theta + sin^(2) theta) + b^(2) (sin^(2) theta + cos ^(2) theta)= (a^(2) +b^(2)) .` Thus, ` (a cos theta - b sin theta)^(2) + (a sin theta + b cos theta)^(2) = (a^(2) + b^(2)) ` `rArr c^(2) + (a sin theta + b cos theta)^(2) = (a^(2) + b^(2)) ` `rArr (a sin theta + b cos theta)^(2) = (a^(2) + b^(2) - c^(2))` ` rArr (a sin theta + b cos theta ) = pm sqrt(a^(2) + b^(2) - c^(2)). ` Hence, `(a sin theta + b cos theta) = pm sqrt(a^(2) + b^(2) - c^(2)). ` |
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