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InterviewSolution
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If `costheta +sin theta= sqrt(2)cos theta`, then prove that` costheta-sintheta =sqrt(2)sin theta` |
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Answer» Given that , `costheta+sintheta=sqrt(2)costheta` ` rArrsintheta=sqrt(2)costheta-costheta` `rArrsintheta=(sqrt(2)-1)costheta` Multiply both sides by `(sqrt(2)+1)` `(sqrt(2)+1)sintheta=(sqrt(2)+1)(sqrt(2)-1)costheta` `rArrsqrt(2)sintheta+sintheta=costheta` `sqrt(2)sintheta=costheta-sintheta` Alternative Method : We have, `costheta+sintheta=sqrt(2)costheta` Squaring both sides , we get `(costheta+sintheta)^(2)=(sqrt2costheta)^(2)` `rArrcos^(2)theta+sin^(2)theta+2costhetasintheta=2cos^(2)theta` `rArr2cos^(2)theta-cos^(2)theta-sin^(2)theta=2sinthetacostheta` `rArr cos^(2)theta-sin^(2)theta=2sinthetacostheta` `rArr(costheta-sintheta)(costheta+sintheta)=2sinthetacostheta` `rArr(costheta-sintheta)*sqrt(2)costheta=2sinthetacostheta` `:. costheta-sintheta=sqrt(2)sintheta` |
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