If x=(1/5) the value of cos((cos)- 1 x + 2 (sin)- 1 x) is

Question

If x=(1/5) the value of cos((cos)- 1 x + 2 (sin)- 1 x) is (A) -√(24/25) (B) √(24/25) (C) -(1/5) (D) (1/5)

Tardigrade Admin · Accepted Answer

The given expression is equal to cos((cos)- 1 x + (sin)- 1 x + (sin)- 1 x) =cos((π /2) + (sin)- 1 x)=-sin((sin)- 1 x)=-x=-(1/5) [Using cos- 1 x + sin- 1 x = (π /2)]

Q. If $x = \frac{1}{5}$ the value of $cos ((cos)^{- 1} x + 2 (s in)^{- 1} x)$ is

$- \frac{24}{25}$

$\frac{24}{25}$

$- \frac{1}{5}$

$\frac{1}{5}$

The given expression is equal to
$cos ((cos)^{- 1} x + (s in)^{- 1} x + (s in)^{- 1} x)$
$= cos (\frac{π}{2} + (s in)^{- 1} x) = - s in ((s in)^{- 1} x) = - x = - \frac{1}{5}$
$[U s in g co s^{- 1} x + s i n^{- 1} x = \frac{π}{2}]$

Q. If x=51​ the value of cos((cos)−1x+2(sin)−1x) is

−2524​​

2524​​

−51​

51​