The value of sec [ sin -1(- sin (50 π/9))+ cos -1 cos (-(31 π/9))] is equal to -

Question

The value of sec [ sin -1(- sin (50 π/9))+ cos -1 cos (-(31 π/9))] is equal to - (A)  sec (10 π/9) (B)  sec (π/9) (C) 1 (D) -1

Tardigrade Admin · Accepted Answer

sec [ sin -1(- sin (50 π/9))+ cos -1 cos (-(31 π/9))] = sec [- sin -1( sin (50 π/9))+ cos -1 cos ((31 π/9))] = sec [- sin -1(- sin (4 π/9))+ cos -1(- cos (4 π/9))] = sec [(4 π/9)+π-(4 π/9)]= sec π=-1

Q. The value of $sec [sin^{- 1} (- sin \frac{50 π}{9}) + cos^{- 1} cos (- \frac{31 π}{9})]$ is equal to -

$sec \frac{10 π}{9}$

$sec \frac{π}{9}$

1

$- 1$

$sec [sin^{- 1} (- sin \frac{50 π}{9}) + cos^{- 1} cos (- \frac{31 π}{9})]$
$= sec [- sin^{- 1} (sin \frac{50 π}{9}) + cos^{- 1} cos (\frac{31 π}{9})]$
$= sec [- sin^{- 1} (- sin \frac{4 π}{9}) + cos^{- 1} (- cos \frac{4 π}{9})]$
$= sec [\frac{4 π}{9} + π - \frac{4 π}{9}] = sec π = - 1$

Q. The value of sec[sin−1(−sin950π​)+cos−1cos(−931π​)] is equal to -

sec910π​

sec9π​

1

−1

sec[sin−1(−sin950π​)+cos−1cos(−931π​)] =sec[−sin−1(sin950π​)+cos−1cos(931π​)] =sec[−sin−1(−sin94π​)+cos−1(−cos94π​)] =sec[94π​+π−94π​]=secπ=−1

Q. The value of $sec [sin^{- 1} (- sin \frac{50 π}{9}) + cos^{- 1} cos (- \frac{31 π}{9})]$ is equal to -

$sec \frac{10 π}{9}$

$sec \frac{π}{9}$

$- 1$

$sec [sin^{- 1} (- sin \frac{50 π}{9}) + cos^{- 1} cos (- \frac{31 π}{9})]$
$= sec [- sin^{- 1} (sin \frac{50 π}{9}) + cos^{- 1} cos (\frac{31 π}{9})]$
$= sec [- sin^{- 1} (- sin \frac{4 π}{9}) + cos^{- 1} (- cos \frac{4 π}{9})]$
$= sec [\frac{4 π}{9} + π - \frac{4 π}{9}] = sec π = - 1$