is cos sino a b 29. If =sinethen :" a b " sec 20' cosec20 -+ is equal to

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( begin{aligned} frac{cos theta}{a}=frac{sin theta}{b} &=k Rightarrow cos theta=a k ; sin theta=b k cos ^{2} theta+sin ^{2} theta=1 & Rightarrow k^{2}=frac{1}{a^{2}+b^{2}} frac{a}{sec 2 theta}+frac{b}{cos alpha^{2} theta} &=operatorname{acos} 2 theta+b sin 2 theta &=aleft(2 cos ^{2} theta-1right)+2 b sin theta cos theta &=aleft(2 a^{2} k^{2}-1right)+2 b^{2} a k^{2} &=2 a^{3} k^{2}-a+2 b^{2} a k^{2} &=2 a^{2} aleft(a^{2}+b^{2}right)-a &=a end{aligned} )

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