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If cosy=xcos(a+y) , where cosa!=-1 , pro...

If `cosy=xcos(a+y)` , where `cosa!=-1` , prove that `(dy)/(dx)=(cos^2(a+y))/(sina)`

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To solve the problem, we start with the equation given: \[ \cos y = x \cos(a + y) \] where \( \cos a \neq -1 \). We need to prove that ...
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If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+y))/(sina) .

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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y^x+x^y+x^x=a^b , find (dy)/(dx) .

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  2. If (cosx)^y=(cosy)^x find (dy)/(dx) .

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  3. If cosy=xcos(a+y) , where cosa!=-1 , prove that (dy)/(dx)=(cos^2(a+y))...

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  4. If (x-y) \ e^(x/(x-y))=a , prove that y(dy)/(dx)+x=2y .

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  5. If x=e^(x//y) , prove that (dy)/(dx)=(x-y)/(xlogx)

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  6. If y=x^(tanx)+sqrt((x^2+1)/2) , find (dy)/(dx)

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  7. If y=1+alpha/((1/x-alpha))+(beta//x)/((1/x-1)(1/x-beta))+(gamma//x^2)...

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  8. If y=x^x^x^(((dotoo))) , find (dy)/(dx) .

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  9. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo))) , prove that (dy)/(d...

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  10. "If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y...

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  11. If y=e^(x+e^(x+e^(x+dotto\ oo))) , show that (dy)/(dx)=y/(1-y) .

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  12. If y=(sqrt(x))^(sqrt(x))^(((sqrt(x))dotoo)) , show that (dy)/(dx)=(y^2...

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  13. If y=x+1/(x+1/(x+1/(x+\ dot))) , prove that (dy)/(dx)=y/(2y-x) .

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  14. If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+\ ddotto\ oo)))) , prove ...

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  15. If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo))) , prove that (dy)/(dx)=1/(2\ ...

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  16. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+\ dotto\ oo))) , prove that (dy)/(d...

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  17. If y=sqrt(logx+sqrt(logx+sqrt(logx+\ dotto\ oo))) , prove that (2y-1)(...

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  18. If y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dotto\ oo))) , prove that (dy)/(d...

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  19. If y=(sinx)^(sinx^(sinx dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-y...

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  20. cos 6x=32 cos^6 x -48cos^4 x + 18 cos^2 x -1

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