Let f(α)= sin -1( sin α)+ cos -1( cos α) and g(β)= sin -1( sin β)+ tan -1( tan β), then find the value of f(100)+g(8).

Question

Let f(α)= sin -1( sin α)+ cos -1( cos α) and g(β)= sin -1( sin β)+ tan -1( tan β), then find the value of f(100)+g(8). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f (100)= sin -1 sin 100+ cos -1 cos 100 sin -1 sin (100-32 π)+ cos -1 cos (32 π-100)=100-32 π+32 π-100=0 g (8)= sin -1 sin 8+ tan -1 tan 8= sin -1 sin (3 π-8)+ tan -1 tan (8-3 π)=0 ∴ f (100)+ g (8)=0

Q. Let $f (α) = sin^{- 1} (sin α) + cos^{- 1} (cos α)$ and $g (β) = sin^{- 1} (sin β) + tan^{- 1} (tan β)$ , then find the value of $f (100) + g (8)$ .

$f (100) = sin^{- 1} sin 100 + cos^{- 1} cos 100$
$sin^{- 1} sin (100 - 32 π) + cos^{- 1} cos (32 π - 100) = 100 - 32 π + 32 π - 100 = 0$
$g (8) = sin^{- 1} sin 8 + tan^{- 1} tan 8 = sin^{- 1} sin (3 π - 8) + tan^{- 1} tan (8 - 3 π) = 0$
$∴ f (100) + g (8) = 0$

Q. Let f(α)=sin−1(sinα)+cos−1(cosα) and g(β)=sin−1(sinβ)+tan−1(tanβ), then find the value of f(100)+g(8).

f(100)=sin−1sin100+cos−1cos100 sin−1sin(100−32π)+cos−1cos(32π−100)=100−32π+32π−100=0 g(8)=sin−1sin8+tan−1tan8=sin−1sin(3π−8)+tan−1tan(8−3π)=0 ∴f(100)+g(8)=0

Q. Let $f (α) = sin^{- 1} (sin α) + cos^{- 1} (cos α)$ and $g (β) = sin^{- 1} (sin β) + tan^{- 1} (tan β)$ , then find the value of $f (100) + g (8)$ .

$f (100) = sin^{- 1} sin 100 + cos^{- 1} cos 100$
$sin^{- 1} sin (100 - 32 π) + cos^{- 1} cos (32 π - 100) = 100 - 32 π + 32 π - 100 = 0$
$g (8) = sin^{- 1} sin 8 + tan^{- 1} tan 8 = sin^{- 1} sin (3 π - 8) + tan^{- 1} tan (8 - 3 π) = 0$
$∴ f (100) + g (8) = 0$