cos -1( cos (-5))+ sin -1( sin (6))- tan -1( tan (12)) is equal to: (The inverse trigonometric functions take the principal values)

Question

cos -1( cos (-5))+ sin -1( sin (6))- tan -1( tan (12)) is equal to: (The inverse trigonometric functions take the principal values) (A) 3 π-11 (B) 4 π-9 (C) 4 π-11 (D) 3 π+1

Tardigrade Admin · Accepted Answer

cos -1( cos (-5))+ sin -1( sin (6))- tan -1( tan (12)) ⇒ (2 π-5)+(6-2 π)-(12-4 π) ⇒ 4 π-11

Q. $cos^{- 1} (cos (- 5)) + sin^{- 1} (sin (6)) - tan^{- 1} (tan (12))$ is equal to :
(The inverse trigonometric functions take the principal values)

$3 π - 11$

$4 π - 9$

$4 π - 11$

$3 π + 1$

$cos^{- 1} (cos (- 5)) + sin^{- 1} (sin (6)) - tan^{- 1} (tan (12))$
$\Rightarrow (2 π - 5) + (6 - 2 π) - (12 - 4 π)$
$\Rightarrow 4 π - 11$

Q. cos−1(cos(−5))+sin−1(sin(6))−tan−1(tan(12)) is equal to : (The inverse trigonometric functions take the principal values)

3π−11

4π−9

4π−11

3π+1