if y=cos^-1((3+5cosx)/(5+3cosx)) then prove that cosx=(4-5y1)/3y1 - Maths - Continuity and Differentiability

Question

if y=cos^-1((3+5cosx)/(5+3cosx)) then prove that cosx=(4-5y1)/3y1

Ghanshyam Dhakar · Accepted Answer

Dear
student,

y= cos-13+5cosx5+3cosx⇒cosy =3+5cosx5+3cosx  
1   and     siny  = 1-cos2y=1-3+5cosx5+3cosx2   
2Differentiate 1 w r t
 x-siny dydx = 5+3cosx-5sinx-3+5cosx-3sinx5+3cosx2⇒-siny dydx = -sinx25+15cosx-9+15cosx5+3cosx2⇒siny dydx = 16sinx5+3cosx2put the value of siny from 2, we get5+3cosx2-3+5cosx25+3cosx y1=16sinx5+3cosx2⇒25+9cos2x+30cosx-9-25cos2x-30cosx5+3cosx y1=16sinx5+3cosx2⇒16-16cos2x5+3cosxy1=16sinx5+3cosx2⇒4sinx5+3cosxy1=16sinx5+3cosx2⇒y15+3cosx = 4⇒3y1cosx = 4-5y1⇒cosx = 4-5y13y1 
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