Answer each of the following questions in one word or one sentence or as per exact requirement of the question: Write the value of A mathematical expression for the cosine of a sum of inverse trigonometric functions: cos(sin^-1 x + cos^-1 x), with the condition |x|

Q49 of 303 Page 4

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of

Given |x| ≤ 1

⇒ ± x ≤ 1

⇒ x ≤ 1 or –x ≤ 1

⇒ x ≤ 1 or x ≥ -1

⇒ x ∈ [-1, 1]

Now also given cos (sin^-1 x + cos^-1 x)

We know that sin^-1 x + cos^-1 x = π/2

∴ cos (sin^-1 x + cos^-1 x) = cos (π/2) = 0

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of .

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of .

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of the expression , when .

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the principal value of .