If √(1-x8) + √(1-y8) =a(x4-y4) st dy/dx =(x3√(1-y8))/( y3√(1-x8)) - Maths - Application of Derivatives

Question

If √(1-x8) + √(1-y8)
=a(x4-y4) st dy/dx
=(x3√(1-y8))/(
y3√(1-x8))

Lovina Kansal · Accepted Answer

Dear student
1-x8+1-y8=ax4-y4Putting x4=sinA and y4= sinB in the given relation we get,1-sin2A+1-sin2B=asinA-sinB⇒cosA+cosB=asinA-sinB⇒2cosA+B2cosA-B2=2asinA-B2cosA+B2⇒cotA-B2=a⇒A-B2=cot-1a⇒A-B=2cot-1a⇒sin-1x4-sin-1y4=2cot-1aDifferentiating both sides w
r t
x, we get,11-x8×ddxx4-11-y8×ddxy4=0⇒11-x8×4x3-11-y8×4y3=0⇒dydx=x3y31-y81-x8
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