Math, asked by lovelies68, 8 months ago

plzzzz Solve plzz.. ​

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Answered by BrainlyEmpire
12

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}}

Answered by MissLuxuRiant
1

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}

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