Question

Write principal value of
${ \sin}^{ - 1} ( - \frac{ \sqrt{3} }{2} ) + \cos ^{ - 1} ( - \frac{1}{2} ) + \tan^{ - 1} ( - \frac{ 1 }{ \sqrt{3} } )$
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Answer 1

Answer:

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Let sin-1(-√3/2) = x and cos-1(-1/2) =

⇒ sin x = (-√3/ 2) and cos y = -1/2

We know that the range of the principal value branch of sin-1 is (-π/2, π/2) and cos-1 is (0, π).

We also know that sin (-π/ 3) = (-√3/ 2) and cos (2π/3) = -1/2

∴ Value of sin-1 (-√3 /2) + cos-1(-1/2) = -π/3 + 2π/3 = π/3

Answer 2

Answer:

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Let sin-1(-√3/2) = x and cos-1(-1/2) =

⇒ sin x = (-√3/ 2) and cos y = -1/2

We know that the range of the principal value branch of sin-1 is (-π/2, π/2) and cos-1 is (0, π).

We also know that sin (-π/ 3) = (-√3/ 2) and cos (2π/3) = -1/2

• ∴ Value of sin-1 (-√3 /2) + cos-1(-1/2) = -π/3 + 2π/3 = π/3

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