find the value of x : sin-1x + sin-1(1-x) = cos-1x Share with your friends Share 73 Manbar Singh answered this We have,sin-1x + sin-11 - x = cos-1x⇒ sin-1x - cos-1x = -sin-11 - x⇒ sin-1x - cos-1x = sin-1x - 1 ........1 as sin-1-x = -sin-1xPut sin-1x = θ and cos-1x = ϕ⇒ sin θ = x and cos ϕ = xThen, cos θ = 1 - sin2θ and sin ϕ = 1 - cos2ϕ⇒ cos θ = 1 - x2 and sin ϕ = 1 - x2Applying the formula:sin θ - ϕ = sin θ cos ϕ - cos θ sin ϕ⇒ sin θ - ϕ = x.x - 1 - x2 . 1 - x2⇒ sin θ - ϕ = x2 - 1 - x2⇒ sin θ - ϕ = x2 - 1 + x2⇒ sin θ - ϕ = 2x2 - 1⇒ θ - ϕ = sin-12x2 - 1⇒ sin-1x - cos-1x = sin-12x2 - 1 ............2 Hence, from 1 and 2 sin-12x2 - 1 = sin-1x - 1⇒ 2x2 - 1 = x - 1⇒ 2x2 - x - 1 + 1 = 0⇒ 2x2 - x = 0⇒ x 2x - 1 = 0Either x = 0 or 2x - 1 = 0Either x = 0 or x = 12 285 View Full Answer
