SOLUTION: If {{{(sinA+cosA)/sinAcosA=1/3}}} What is the value of {{{sin^4(A)-cos^4(A)}}}?

Question 1133311: If
What is the value of ?
Answer by ikleyn(52903) (Show Source): You can put this solution on YOUR website!
.

I will solve it in two steps.

Step 1

For brevity, let's denote x = sin(A)*cos(A).


 =   ====>  square both sides  ====>  


 =  =   ====>


9*(1 + 2x) = 

 = 0

 =  = .


Since the modulus of x,  |x|, must be less than 1, only the root   x =   is the solution.


It implies  2x = 2*sin(A)*cos(A) = sin(2A) =  = .      (1)

Step 2

 = .  ====>  replace    by 1  ====>


 =  =  = .


Substitute here   from (1)  and continue


 =  =  =  =  = 


=  = -0.228 (approximately, with 3 correct decimal places).


ANSWER.  If   = ,  then   =  = -0.228 (approximately, with 3 correct decimal places).

Solved.

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