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If `cosx+cos^(2)x=1` , the numberical value of(यदि `cosx+cos^(2)x=1` है तो का अंकित मान क्या होगा )A. `-1`B. 2C. 0D. 1 |
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Answer» Correct Answer - c `cos theta+sintheta=sqrt(2)cos theta` Squaring both sides `cos^(2)theta+sin^(2)theta+2cos thetasintheta=2cos^(2)theta` `rArr 2cos^(2)theta-cos^(2)theta-sin^(2)theta=2` `cos theta sintheta` `rArrcos^(2)theta-sin^(20theta=2sin theta cos theta` `rArr(cos theta-sin theta)(sqrt(2)cos theta)=` `2sin theta.cos theta` `rArr(cos theta-sin theta)=(2sinthetacos theta)/(sqrt(2costheta))` Alternate Let `sqrt(2)cos theta=alpha` `therefore cos theta+-sin theta=a` `cos thea+-sintheta=sqrt(2-a^(2))` `=sqrt(2(1-cos^(2)theta))` `=sqrt(2sin^(2)theta)=sqrt(2)sin theta` |
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