cos-1 ((-1/2))-2 sin-1((1/2))+3 cos-1((-1/√2))-4 tan-1 (-1) equals

Question

cos-1 ((-1/2))-2 sin-1((1/2))+3 cos-1((-1/√2))-4 tan-1 (-1) equals (A) (19π/12) (B) (35π/12) (C) (47π/12) (D) (43π/12)

Tardigrade Admin · Accepted Answer

cos -1(-(1/2))-2 sin -1((1/2))+3 cos -1(-(1/√2))-4 tan -1(-1) =π- cos -1((1/2))-2((π/6))+3(π- cos -1((1/√2)))+4 tan -1(1) =π-(π/3)-(π/3)+3(π-(π/4))+4 . (π/4) =(π/3)+3 π-(3 π/4)+π =(43 π/12)

Q. $co s^{- 1} (\frac{- 1}{2}) - 2 s i n^{- 1} (\frac{1}{2}) + 3 co s^{- 1} (\frac{- 1}{2}) - 4 t a n^{- 1} (- 1)$ equals

$\frac{19 π}{12}$

$\frac{35 π}{12}$

$\frac{47 π}{12}$

$\frac{43 π}{12}$

Q. cos−1(2−1​)−2sin−1(21​)+3cos−1(2​−1​)−4tan−1(−1) equals

1219π​

1235π​

1247π​

1243π​

cos−1(−21​)−2sin−1(21​)+3cos−1(−2​1​)−4tan−1(−1) =π−cos−1(21​)−2(6π​)+3(π−cos−1(2​1​))+4tan−1(1) =π−3π​−3π​+3(π−4π​)+4.4π​ =3π​+3π−43π​+π =1243π​

Q. $co s^{- 1} (\frac{- 1}{2}) - 2 s i n^{- 1} (\frac{1}{2}) + 3 co s^{- 1} (\frac{- 1}{2}) - 4 t a n^{- 1} (- 1)$ equals

$\frac{19 π}{12}$

$\frac{35 π}{12}$

$\frac{47 π}{12}$

$\frac{43 π}{12}$