Expert: Paul Klarreich - 10/4/2007

Question
differentiate sinx+cosx=1.5 w.r.t cosx

Answer
Questioner:   vishnu
Category:  Calculus
Private:  No
 
Subject:  differentiation
Question:  differentiate sinx+cosx=1.5 w.r.t cosx
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Hi, Vish,

This seems strange, but suppose we let  U = cos x

Then  sin x = sqrt(1 - U^2)  and we have the equation:

sqrt(1 - U^2) + U = constant.

Differentiate with respect to U:
  -2U
--------------  + 1 = 0
2sqrt(1 - U^2)

   - U
--------------  + 1 = 0
sqrt(1 - U^2)

You could do some simplifying:

   - U
--------------  = - 1
sqrt(1 - U^2)

- U = - sqrt(1 - U^2)

U = sqrt(1 - U^2)

cos x = sin x

Strange, but true???