The value of sin- 1 sin⁡17+cos- 1⁡cos⁡10 is equal to

Question

The value of sin- 1 sin⁡17+cos- 1⁡cos⁡10 is equal to (A) 27 (B) -27 (C) 17-5π  (D) 9π -27

Tardigrade Admin · Accepted Answer

sin -1 sin 17= sin -1 sin (17-5 π+5 π) =5 π-17 cos -1( cos 10)= cos -1 cos (10-3 π+3 π) = cos -1 cos 3 π+(10-3 π) = cos -1 - cos (10-3 π) =π- cos -1 cos (10-3 π) =π-(10-3 π)=4 π-10 Hence, sin -1 sin 17+ cos -1( cos 10)=9 π-27

Q. The value of $s i n^{- 1} s in 17 + co s^{- 1} cos 10$ is equal to

$27$

$- 27$

$17 - 5 π$

$9 π - 27$

Q. The value of sin−1sin⁡17+cos−1⁡cos⁡10 is equal to

27

−27

17−5π

9π−27

sin−1sin17=sin−1sin(17−5π+5π) =5π−17 cos−1(cos10)=cos−1cos(10−3π+3π) =cos−1cos{3π+(10−3π)} =cos−1{−cos(10−3π)} =π−cos−1cos(10−3π) =π−(10−3π)=4π−10 Hence, sin−1sin17+cos−1(cos10)=9π−27

Q. The value of $s i n^{- 1} s in 17 + co s^{- 1} cos 10$ is equal to

$27$

$- 27$

$17 - 5 π$

$9 π - 27$