Question

Now, 44. If a cos 2x+b sin 2x =chas a and B as its roots, then prove that (i) tan a+tan B = 20 INCERT EXEMPLAR] (ii) tan a tanB = tan (a +B) a +C C + (iii) tan (a +B) = 2 INCERT EXEMPLAR] 45. We have, cos (cosa +

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

We have, ( a cos 2 theta+b sin 2 theta=c ) ( Rightarrow quad aleft(frac{1-tan ^{2} theta}{1+tan ^{2} theta}right)+bleft(frac{2 tan theta}{1+tan ^{2} theta}right)=c ) ( Rightarrow quad aleft(1-tan ^{2} thetaright)+2 b tan theta=cleft(1+tan ^{2} thetaright) ) ( Rightarrow quad(c+a) tan ^{2} theta-2 b tan theta+c-a=0 ) Equation (i) has roots ( alpha ) and ( beta ) Thus, equation (ii) has roots tan ( alpha ) and ( tan beta ) ( therefore ) Sum of roots, ( tan alpha+tan beta=frac{-(-2 b)}{a+c}=frac{2 b}{a+c} )