Question

Can the domain of
${ \cos}^{ - 1} (x)$
be restricted to [-π,0] ? If yes then how?​

Answer 1

cos^-1 (x) [−1,1]

here the domain is [-1,1]

Answer 2

Answer:

Property 1

sin-1 (1/x) = cosec-1x , x ≥ 1 or x ≤ -1

cos-1 (1/x) = sec-1x , x ≥ 1 or x ≤ -1

tan-1 (1/x) = cot-1x , x > 0

Proof : sin-1 (1/x) = cosec-1x , x ≥ 1 or x ≤ -1,

Let sin−1x=y

i.e. x = cosec y

1x=siny

sin−11x)=y

sin−11x)=cosec−1x

sin−1(1x)=cosec−1x

Hence, sin−11x=cosec−1x where, x ≥ 1 or x ≤ -1.

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