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Class 12th Chapter 1 Differentiation Exercise 1.3 Question 4 .(iii) #MSB

iii. secx5+y5x5-y5=a2
Sol. x5+y5x5-y5=sec-1a2
Let k= sec-1a2
=x5+y5x5-y5=k
=x5+y5=k(x5-y5)
⇒y5+ky5=kx5-x5
⇒y5(k+1)=x5(k-1)
⇒k-1k+1=y5x5  -(eq. A)
Differentiating y w.r.t x
⇒(k+1).5y4×dydx=(k-1)×5.x4
⇒dydx=k-1k+1×x4y4
⇒dydx=y5x5×x4y4=yx  From Eq. A
Hence Proved.