Question

Sin inverse x + cos inverse x =π/2

Answer 1

Answer:

sin-¹ (x) + cos-¹ (x) = π/2 , x ∈ [ -1 , 1 ].

Step-by-step explanation:

sin-¹ (x) + cos-¹ (x) = π/2 , x ∈ [ -1 , 1 ].

Here, x ∈ [ -1 , 1 ].

Let sin-¹ x = θ. Then θ ∈ [ -π/2 , π/2 ] and sin θ = x

Note that -π/2 ≤ θ ≤ π/2 ⇔ 0 ≤ π/2 - θ ≤ π

So, cos ( π/2 - θ ) = sin θ = x,

which gives cos-¹ x = π/2 - θ = π/2 - sin-¹ x

Hence, sin-¹ (x) + cos-¹ (x) = π/2 , |x| ≤ 1.