Solution set of the equation, cos -1 x- sin -1 x= cos -1(x √3)

Question

Solution set of the equation, cos -1 x- sin -1 x= cos -1(x √3) (A) is a unit set (B) consists of two elements (C) consists of three elements (D) is a void set

Tardigrade Admin · Accepted Answer

cos -1 x+ sin -1 x=(π/2) ; on subtraction, 2 sin -1 x=(π/2)- cos -1(x √3)= sin -1(x √3) ⇒ 2 α=β ⇒ 2 sin α cos α= sin β ⇒ x=0, ± 1 / 2

Q. Solution set of the equation, $cos^{- 1} x - sin^{- 1} x = cos^{- 1} (x 3)$

is a unit set

consists of two elements

consists of three elements

is a void set

$cos^{- 1} x + sin^{- 1} x = \frac{π}{2};$ on subtraction, $2 sin^{- 1} x = \frac{π}{2} - cos^{- 1} (x 3) = sin^{- 1} (x 3)$
$\Rightarrow 2 α = β \Rightarrow 2 sin α cos α = sin β \Rightarrow x = 0, \pm 1/2$

Q. Solution set of the equation, cos−1x−sin−1x=cos−1(x3​)