The value of cos [(1/2) cos -1( cos (-(14 π/5)))] is/are -

Question

The value of cos [(1/2) cos -1( cos (-(14 π/5)))] is/are - (A)  cos (-(7 π/5)) (B)  sin ((π/10)) (C)  cos ((2 π/5)) (D) - cos ((3 π/5))

Tardigrade Admin · Accepted Answer

cos [(1/2) cos -1 cos (2 π+(4 π/5))] = cos ((1/2) × (4 π/5))= cos (2 π/5) = cos (π-(3 π/5))=- cos ((3 π/5)) cos (2 π/5)= sin ((π/2)-(2 π/5))= sin ((π/10))

Q. The value of $cos [\frac{1}{2} cos^{- 1} (cos (- \frac{14 π}{5}))]$ is/are -

$cos (- \frac{7 π}{5})$

$sin (\frac{π}{10})$

$cos (\frac{2 π}{5})$

$- cos (\frac{3 π}{5})$

$cos [\frac{1}{2} cos^{- 1} cos (2 π + \frac{4 π}{5})]$
$= cos (\frac{1}{2} \times \frac{4 π}{5}) = cos \frac{2 π}{5}$
$= cos (π - \frac{3 π}{5}) = - cos (\frac{3 π}{5})$
$& cos \frac{2 π}{5} = sin (\frac{π}{2} - \frac{2 π}{5}) = sin (\frac{π}{10})$

Q. The value of cos[21​cos−1(cos(−514π​))] is/are -

cos(−57π​)

sin(10π​)

cos(52π​)

−cos(53π​)