Question

plzzzz Solve plzz.. ​

Answer 1

Given that,

$\sf \: x = sin {}^{ - 1} (sin10) \\ \sf \: y = {cos}^{ - 1} (cos10)$

Now,

$\sf \: sin(y - x) = sin(y)cos(x) - cos(y)sin(x) \\ \\ \longrightarrow \: \sf \: sin(y - x) = sin \{cos {}^{ - 1} (cos10) \}cos \{sin {}^{ - 1}(sin10) \} - \: cos\{cos {}^{ - 1} (cos10) \}sin \{sin {}^{ - 1}(sin10) \} \\ \\ \longrightarrow \: \sf \: sin(y - x) = cos10sin10 - sin10cos10 \\ \\ \longrightarrow \: \sf \: sin(y - x) = 0 \\ \\ \longrightarrow \: \sf \: sin(y - x) = \sin(\pi) \\ \\ \longrightarrow \boxed{ \boxed{\sf \: y - x = \pi}}$

Answer 2

Given that,

$\begin{gathered} \sf \: x = sin {}^{ - 1} (sin10) \\ \sf \: y = {cos}^{ - 1} (cos10) \end{gathered}$

Now,

$\begin{gathered} \sf \: sin(y - x) = sin(y)cos(x) - cos(y)sin(x) \\ \\ \longrightarrow \: \sf \: sin(y - x) = sin \{cos {}^{ - 1} (cos10) \}cos \{sin {}^{ - 1}(sin10) \} - \: cos\{cos {}^{ - 1} (cos10) \}sin \{sin {}^{ - 1}(sin10) \} \\ \\ \longrightarrow \: \sf \: sin(y - x) = cos10sin10 - sin10cos10 \\ \\ \longrightarrow \: \sf \: sin(y - x) = 0 \\ \\ \longrightarrow \: \sf \: sin(y - x) = \sin(\pi) \\ \\ \longrightarrow \boxed{ \boxed{\sf \: y - x = \pi}}\end{gathered}$