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Solve: `cottheta``+cos e ctheta=sqrt(3)` |
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Answer» Correct Answer - `theta=2n pi+pi/3, n in Z` `cot theta + cosec theta = sqrt(3)` or `(cos theta)/(sin theta)+1/(sin theta)=sqrt(3)` or `cos theta +1 = sqrt(3) sin theta` or `sqrt(3) sin theta - cos theta=1` ...(i) or `2 cos (theta +pi/3)=-1` or `cos (theta + pi/3)=-1/2` or `cos (theta + pi/3)= "cos" (2 pi)/3` `rArr theta +pi/3=2 n pi pm (2pi)/3, n in Z` or `theta = 2n pi pm (2pi)/3 - pi/3, n in Z` `:. theta =2npi +pi/3, n in Z` or `theta =2 n pi - pi =(2n-1) pi, n in Z` But `theta` cannot be equal to `(2n-1)pi` as it makes `sin theta=0`. Hence, `theta=2n pi +pi/3, in Z`. |
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