If x=sin(2 t a n- 1 3) and y=sin((1/2) (tan)- 1 (4/3)), then

Question

If x=sin(2 t a n- 1 3) and y=sin((1/2) (tan)- 1 (4/3)), then (A) 2x=1-y (B) x2=1-2y (C) x2=1+y (D) y2=2x-1

Tardigrade Admin · Accepted Answer

Let, x=sin 2θ (where tan θ =3 ) ⇒ x=(2 tan θ /1 + t a n2 θ )=(6/1 + 9)=(3/5) If α =tan- 1(4/3) ⇒ y=sin((α /2))=(1/√2)√1 - cos α =(1/√2)√1 - (3/5)=(1/√5) ∴ y2=(1/5)⇒ y2=2x-1

Q. If $x = s in (2 t a n^{- 1} 3)$ and $y = s in (\frac{1}{2} (t an)^{- 1} \frac{4}{3}),$ then

$2 x = 1 - y$

$x^{2} = 1 - 2 y$

$x^{2} = 1 + y$

$y^{2} = 2 x - 1$

Q. If x=sin(2tan−13) and y=sin(21​(tan)−134​), then

2x=1−y

x2=1−2y

x2=1+y

y2=2x−1

Let, x=sin2θ (where tanθ=3 ) ⇒x=1+tan2θ2tanθ​=1+96​=53​ If α=tan−134​ ⇒y=sin(2α​)=2​1​1−cosα​ =2​1​1−53​​=5​1​ ∴y2=51​⇒y2=2x−1

Q. If $x = s in (2 t a n^{- 1} 3)$ and $y = s in (\frac{1}{2} (t an)^{- 1} \frac{4}{3}),$ then

$2 x = 1 - y$

$x^{2} = 1 - 2 y$

$x^{2} = 1 + y$

$y^{2} = 2 x - 1$