If α= sin ( cot -1( tan ( cos -1 (2/3)))) and β= sin ( operatornamecosec-1( cot ( tan -1 (1/3)))) are the roots of the quadratic equation ax 2+ bx + c =0 where a , b , c are integers and c is prime then the value of ( a + b + c ) equals

Question

If α= sin ( cot -1( tan ( cos -1 (2/3)))) and β= sin ( operatornamecosec-1( cot ( tan -1 (1/3)))) are the roots of the quadratic equation ax 2+ bx + c =0 where a , b , c are integers and c is prime then the value of ( a + b + c ) equals (A) 1 (B) 2 (C) 3 (D) 9

Tardigrade Admin · Accepted Answer

α=(2/3) ; β=(1/3). Hence the quadratic equation whose roots are α and β. x 2- x +(2/9)=0 ⇒ 9 x 2-9 x +2=0 a + b + c =2

Q. If $α = sin (cot^{- 1} (tan (cos^{- 1} \frac{2}{3})))$ and $β = sin (cosec^{- 1} (cot (tan^{- 1} \frac{1}{3})))$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ where $a, b, c$ are integers and $c$ is prime then the value of $(a + b + c)$ equals

1

2

3

9

$α = \frac{2}{3}; β = \frac{1}{3}$ .
Hence the quadratic equation whose roots are $α$ and $β$ .
$x^{2} - x + \frac{2}{9} = 0 \Rightarrow 9 x^{2} - 9 x + 2 = 0$
$a + b + c = 2$

Q. If α=sin(cot−1(tan(cos−132​))) and β=sin(cosec−1(cot(tan−131​))) are the roots of the quadratic equation ax2+bx+c=0 where a,b,c are integers and c is prime then the value of (a+b+c) equals

1

2

3

9

α=32​;β=31​. Hence the quadratic equation whose roots are α and β. x2−x+92​=0⇒9x2−9x+2=0 a+b+c=2

Q. If $α = sin (cot^{- 1} (tan (cos^{- 1} \frac{2}{3})))$ and $β = sin (cosec^{- 1} (cot (tan^{- 1} \frac{1}{3})))$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ where $a, b, c$ are integers and $c$ is prime then the value of $(a + b + c)$ equals

$α = \frac{2}{3}; β = \frac{1}{3}$ .
Hence the quadratic equation whose roots are $α$ and $β$ .
$x^{2} - x + \frac{2}{9} = 0 \Rightarrow 9 x^{2} - 9 x + 2 = 0$
$a + b + c = 2$