Question

23. If cos + sino = m, sece + coseco =n, what is m/n? RRB NTPC (Phase I) 2016 (1) 1 (2) sinocos (3) sec ecosece (4) cotetano

11th - 12th Class

Maths

Solution

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23. (2) Given, ( m=cos theta+sin theta ) and [ n=sec theta+operatorname{cosec} theta ] and [ frac{m}{n}=frac{cos theta+sin theta}{sec theta+operatorname{cosec} theta} ] We know that, ( frac{1}{sec theta}=cos theta, frac{1}{operatorname{cosec} theta}=sin theta ) [ begin{aligned} frac{m}{n} &=frac{cos theta+sin theta}{frac{1}{cos theta}+frac{1}{sin theta}} &=frac{(cos theta+sin theta)}{(cos theta+sin theta)}(cos theta sin theta) &=cos theta sin theta end{aligned} ]