Question

a. Ma la creat color anita me to me we 4. If (cose + cos20)3 = cose + cos20, then the least positive value of 0 is equal to - er in AIBI nla

JEE/Engineering Exams

Maths

Solution

191

4.0 (1 ratings)

( cos ^{3} theta+cos ^{3} 2 theta+3 cos theta cos ^{frac{1}{2}} thetaleft[cos ^{frac{1}{sqrt{2}}}+cos 2 thetaright] ) ( sin ^{3} theta+cos ^{3} 2 ) ( 3 cos theta cos 2 theta[tan theta+cos 2 theta]=0 ) ( operatorname{coth} alpha quad cos theta=0, cos 2 theta=0 ) or ( cos theta+cos 2 theta=0 ) ( cos theta=0 ) gives ( theta=90^{circ} ) ( cos 2 theta=0 ) given ( theta=45^{circ} ) ( cos theta ) Far for ( cos theta+cos 2 theta=0 ) we how ( cos theta=-left[2 cos ^{2} theta-1right] ) ( cos theta=-2 cos ^{2} theta+1 ) ( Rightarrow quad 2 cos ^{2} theta+cos theta-1=0 ) [ operatorname{lot} quad cos ^{2} theta=x-0 ] ( 2 x^{2}+x-1=0 ) Ow distic foummed ( x=frac{-1 pm sqrt{(1)^{2}-4(2)(-1)}}{62 times 2} ) ( Rightarrow x=frac{-1+3}{4} quad x-frac{1-3}{4} ) ( x=frac{-1 pm 3}{4} Rightarrow ) ( x=frac{1}{2} ) or ( x=-1 ) far ( f log m ) (0) ( x=cos ^{2} theta ) So for ( x= ) ( 7 cos theta=pm frac{1}{sqrt{2}} ) 1