Question

49. If tan 0 =cot 20 then the value of O is (A) (2n+1)/6;n el (B) (2n +1) t/6;n el;n 3m+1;m el (C) (2n+1); n e l; n + 2m+1; m € I (D) none

JEE/Engineering Exams

Maths

Solution

128

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( tan theta=cot 2 theta ) ( frac{sin theta}{cos theta}=frac{cos 2 theta}{sin 2 theta} ) ( frac{sin theta}{sin theta}=frac{2 cos ^{2} theta-1}{2 sin theta sin theta} ; theta eq frac{pi}{2}, frac{3 pi}{2}, frac{5 pi}{2} ) ( 2 cos ^{2} theta-2 sin ^{2} theta=1 ) ( cos 2 theta=1 / 2 ) ( 2 theta=2 pi pm pi / 3 ) ( theta=n pi pm pi / 6,0 eq frac{2 n+1}{2} pi ) ( rightarrow operatorname{gh} operatorname{sen}(6) )